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Find the number whose fifth part increased by 5 is equal to its fourth part diminished by 5 .
Three numbers are in the ratio of
4:5:6. If the sum of the largest and the smallest equals the sum of the third and 55 , find the numbers.
If 10 be added to four times a certain number, the result is 5 less than five times the number. Find the number

$5$ . Find the number whose fifth part increased by $5$ is equal to its fourth part diminished by $5$ . $\newline$ $6$ . Three numbers are in the ratio of $4: 5: 6$ . If the sum of the largest and the smallest equals the sum of the third and $55$ , find the numbers. $\newline$ $7$ . If $10$ be added to four times a certain number, the result is $5$ less than five times the number. Find the number

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Weighted averages: word problems

Full solution

Q.

5

. Find the number whose fifth part increased by

5

is equal to its fourth part diminished by

5

.

\newline

6

. Three numbers are in the ratio of

4: 5: 6

. If the sum of the largest and the smallest equals the sum of the third and

55

, find the numbers.

\newline

7

. If

10

be added to four times a certain number, the result is

5

less than five times the number. Find the number

Set up equation for x: Let $x$ be the number we are looking for in the first problem. Set up the equation based on the problem statement: one-fifth of $x$ plus $5$ equals one-fourth of $x$ minus $5$ .
Clear fractions and solve: Clear the fractions by multiplying every term by $20$ , the least common multiple of $4$ and $5$ .
Find numbers using $k$ : Simplify and solve for $x$ .
Simplify and solve for k: For the second problem, let the three numbers be $4$ k, $5$ k, and $6$ k respectively. According to the problem, the sum of the largest and smallest equals the sum of the third and $55$ .
Calculate actual numbers: Simplify and solve for $k$ .
Set up equation for $y$ : Calculate the actual numbers using the value of $k$ .
Simplify and solve for y: For the third problem, let $y$ be the certain number. Set up the equation: $10$ added to four times $y$ equals $5$ less than five times $y$ .
Simplify and solve for $y$ : For the third problem, let $y$ be the certain number. Set up the equation: $10$ added to four times $y$ equals $5$ less than five times $y$ . Simplify and solve for $y$ .

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\newline

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\newline

\square

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