Solving Quantitative Problems $\newline$ g Quantitative Problems

View step-by-step help

Home

Math Problems

Grade 6

One-step inequalities: word problems

Full solution

Q. Solving Quantitative Problems

\newline

g Quantitative Problems

Tom's Wage Calculation: Tom's hourly wage is $10$ Euros. $\newline$ Calculation: $10$ Euros/hour.
Tom's Weekly Earnings: Tom works $8$ hours a day. $\newline$ Calculation: $10$ Euros/hour $\times$ $8$ hours/day = $80$ Euros/day.
Corinna's Hourly Earnings: Tom works $5$ days a week. $\newline$ Calculation: $80$ Euros/day $\times$ $5$ days/week = $400$ Euros/week.
Corinna's Extra Hours: Tom works for $4$ weeks. $\newline$ Calculation: $400$ Euros/week $\times 4$ weeks = $1600$ Euros for $4$ weeks.
Photo Enlargement Ratio: The ratio of concentrate to soft drink is $1:4$ . Calculation: $650 \, \text{litres} \times 4 = 2600 \, \text{litres}$ of soft drink.
Dora's Age Calculation: Corinna earns $25$ Euros per hour for the first $8$ hours each day. $\newline$ Calculation: $25$ Euros/hour $\times$ $8$ hours/day = $200$ Euros/day.
Hanna's Age Calculation: For each hour over $8$ hours, she earns $1.5$ times her hourly wage. $\newline$ Calculation: $25$ Euros/hour $\times 1.5 = 37.5$ Euros for each extra hour.
Total Club Members: Corinna works $5$ days a week. $\newline$ Calculation: $200$ Euros/day $\times$ $5$ days/week = $1000$ Euros/week for the first $8$ hours each day.
Members in One Club: Corinna earns $37.5$ Euros for each extra hour she works per day. $\newline$ Assumption: Corinna works extra hours every day. $\newline$ Calculation: $\frac{37.5 \text{ Euros}}{\text{extra hour}} \times X \text{ extra hours/day} \times 5 \text{ days/week} = Y \text{ Euros/week}$ for extra hours.
Expression Deduction: The original ratio of width to height is $9\,\text{cm}$ to $6\,\text{cm}$ . $\newline$ Calculation: $\frac{9\,\text{cm}}{6\,\text{cm}} = 1.5$ .
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . $\newline$ Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ for the height of the enlarged photo.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . $\newline$ Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. $\newline$ Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. $\newline$ Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $\newline$ $15 + \text{Dora's age} = 20$ . $\newline$ \text{Dora's age} = $20 - 15 = 5$ years.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . $\newline$ Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. $\newline$ Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. $\newline$ Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $\newline$ $15 + \text{Dora's age} = 20$ . $\newline$ \text{Dora's age} = $20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. $\newline$ Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . $\newline$ Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. $\newline$ Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. $\newline$ Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $\newline$ $15 + \text{Dora's age} = 20$ . $\newline$ $\text{Dora's age} = 20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. $\newline$ Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. $\newline$ Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $\newline$ $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $0$ . $\newline$ $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $1$ years.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $15 + \text{Dora's age} = 20$ . \text{Dora's age} = $20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $0$ . \text{Hanna's age} = $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $1$ years.The total number of members in both clubs is $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $2$ . Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $3$ has $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $4$ members, $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $5$ has $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $6$ members, and some are in both clubs.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $15 + \text{Dora's age} = 20$ . \text{Dora's age} = $20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $0$ . \text{Hanna's age} = $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $1$ years.The total number of members in both clubs is $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $2$ . Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $3$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $4$ members, $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $5$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $6$ members, and some are in both clubs.To find the number of members in only one club, subtract the number of members in both clubs from the total. Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $7$ .
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $15 + \text{Dora's age} = 20$ . \text{Dora's age} = $20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $0$ . \text{Hanna's age} = $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $1$ years.The total number of members in both clubs is $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $2$ . Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $3$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $4$ members, $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $5$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $6$ members, and some are in both clubs.To find the number of members in only one club, subtract the number of members in both clubs from the total. Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $7$ .The correct expression is not given directly, but we can deduce it. Calculation: If we add the members of $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $3$ and $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $5$ , we count the members in both clubs twice. So, the expression is $5$ $0$ .
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $15 + \text{Dora's age} = 20$ . \text{Dora's age} = $20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $0$ . \text{Hanna's age} = $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $1$ years.The total number of members in both clubs is $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $2$ . Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $3$ has $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $4$ members, $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $5$ has $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $6$ members, and some are in both clubs.To find the number of members in only one club, subtract the number of members in both clubs from the total. Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $7$ .The correct expression is not given directly, but we can deduce it. Calculation: If we add the members of $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $3$ and $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $5$ , we count the members in both clubs twice. So, the expression is $5$ $0$ .Bottle $5$ $1$ originally contains $5$ $2$ liter of orange juice. Calculation: After pouring, bottle $5$ $1$ has $5$ $4$ liters left.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $15 + \text{Dora's age} = 20$ . \text{Dora's age} = $20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $0$ . \text{Hanna's age} = $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $1$ years.The total number of members in both clubs is $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $2$ . Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $3$ has $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $4$ members, $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $5$ has $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $6$ members, and some are in both clubs.To find the number of members in only one club, subtract the number of members in both clubs from the total. Calculation: $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $7$ .The correct expression is not given directly, but we can deduce it. Calculation: If we add the members of $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $3$ and $\frac{15\,\text{cm}}{1.5} = 10\,\text{cm}$ $5$ , we count the members in both clubs twice. So, the expression is $5$ $0$ .Bottle $5$ $1$ originally contains $5$ $2$ liter of orange juice. Calculation: After pouring, bottle $5$ $1$ has $5$ $4$ liters left.Bottle $5$ $5$ is half as big as bottle $5$ $1$ and is $5$ $7$ full. Calculation: Bottle $5$ $5$ 's volume is $5$ $9$ liters (half of $5$ $1$ ), and it contains $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $1$ liters of orange juice ( $5$ $7$ of $5$ $5$ ).
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $15 + \text{Dora's age} = 20$ . \text{Dora's age} = $20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $0$ . \text{Hanna's age} = $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $1$ years.The total number of members in both clubs is $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $2$ . Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $3$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $4$ members, $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $5$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $6$ members, and some are in both clubs.To find the number of members in only one club, subtract the number of members in both clubs from the total. Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $7$ .The correct expression is not given directly, but we can deduce it. Calculation: If we add the members of $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $3$ and $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $5$ , we count the members in both clubs twice. So, the expression is $5$ $0$ .Bottle $5$ $1$ originally contains $5$ $2$ liter of orange juice. Calculation: After pouring, bottle $5$ $1$ has $5$ $4$ liters left.Bottle $5$ $5$ is half as big as bottle $5$ $1$ and is $5$ $7$ full. Calculation: Bottle $5$ $5$ 's volume is $5$ $9$ liters (half of $5$ $1$ ), and it contains $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $1$ liters of orange juice ( $5$ $7$ of $5$ $5$ ).Bottle $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $4$ is half-full of orange juice. Calculation: Bottle $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $4$ 's volume is the same as bottle $5$ $1$ ( $5$ $2$ liter), so it contains $5$ $9$ liters of orange juice.
Orange Juice Bottles: The width of the enlarged photo is $15\,\text{cm}$ . $\newline$ Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ for the height of the enlarged photo.The average age of Dora and her three siblings is $5$ years. $\newline$ Calculation: $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ years.Calculate Dora's age. $\newline$ Calculation: $(2 + 6 + 7 + \text{Dora's age}) / 4 = 5$ . $\newline$ $15 + \text{Dora's age} = 20$ . $\newline$ $\text{Dora's age} = 20 - 15 = 5$ years.The average age of Dora, Hanna, Emil, Franka, and Gustav is $10$ years. $\newline$ Calculation: $(\text{Dora's age} + \text{Hanna's age} + \text{Emil's age} + \text{Franka's age} + \text{Gustav's age}) / 5 = 10$ years.Calculate Hanna's age. $\newline$ Calculation: $(5 + \text{Hanna's age} + 18 + 6 + 1) / 5 = 10$ . $\newline$ $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $0$ . $\newline$ $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $1$ years.The total number of members in both clubs is $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $2$ . $\newline$ Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $3$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $4$ members, $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $5$ has $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $6$ members, and some are in both clubs.To find the number of members in only one club, subtract the number of members in both clubs from the total. $\newline$ Calculation: $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $7$ .The correct expression is not given directly, but we can deduce it. $\newline$ Calculation: If we add the members of $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $3$ and $15\,\text{cm} / 1.5 = 10\,\text{cm}$ $5$ , we count the members in both clubs twice. So, the expression is $5$ $0$ .Bottle $5$ $1$ originally contains $5$ $2$ liter of orange juice. $\newline$ Calculation: After pouring, bottle $5$ $1$ has $5$ $4$ liters left.Bottle $5$ $5$ is half as big as bottle $5$ $1$ and is $5$ $7$ full. $\newline$ Calculation: Bottle $5$ $5$ 's volume is $5$ $9$ liters (half of $5$ $1$ ), and it contains $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $1$ liters of orange juice ( $5$ $7$ of $5$ $5$ ).Bottle $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $4$ is half-full of orange juice. $\newline$ Calculation: Bottle $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $4$ 's volume is the same as bottle $5$ $1$ ( $5$ $2$ liter), so it contains $5$ $9$ liters of orange juice.Maria fills bottle $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $4$ with water until it is full. $\newline$ Calculation: Bottle $(\text{Anton's age} + \text{Berta's age} + \text{Carl's age} + \text{Dora's age}) / 4 = 5$ $4$ now contains $5$ $9$ liters of orange juice + $5$ $9$ liters of water = $5$ $2$ liter of liquid.

Solving Quantitative Problems\newlineg Quantitative Problems

Solving Quantitative Problems $\newline$ g Quantitative Problems