Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

rrect answer.
The cost of a certain number of pens is
₹72. If the cost of each pen is decreased by then 8 more pens can be purchased for the same amount. How many pens can be purey for the same amount if the cost of each pen is increased by
₹1.50 ?

rrect answer. $\newline$ The cost of a certain number of pens is $₹ 72$ . If the cost of each pen is decreased by then $8$ more pens can be purchased for the same amount. How many pens can be purey for the same amount if the cost of each pen is increased by $₹ 1.50$ ?

View step-by-step help

View step-by-step help

Identify quotients of rational numbers: word problems

Full solution

Q. rrect answer.

\newline

The cost of a certain number of pens is

₹ 72

. If the cost of each pen is decreased by then

8

more pens can be purchased for the same amount. How many pens can be purey for the same amount if the cost of each pen is increased by

₹ 1.50

?

Define $x$ as original cost: Let $x$ be the original cost of each pen. Then the number of pens that can be bought for $\text{₹}72$ is $\frac{72}{x}$ .
Calculate new cost: If the cost of each pen is decreased by ₹ $1$ , then the new cost of each pen is $x - 1$ . So, $8$ more pens can be bought, which means the new number of pens that can be bought for ₹ $72$ is $72/(x - 1)$ .
Formulate equation: According to the problem, the number of pens bought for $\text{₹}72$ at the original price is $8$ less than the number of pens bought at the reduced price. So, we have the equation $\frac{72}{x} + 8 = \frac{72}{x - 1}$ .
Clear denominators: Multiply both sides of the equation by $x(x - 1)$ to clear the denominators: $x(x - 1)(\frac{72}{x} + 8) = x(x - 1)(\frac{72}{x - 1})$ .
Simplify equation: Simplify the equation: $72(x - 1) + 8x(x - 1) = 72x$ .
Combine like terms: Distribute and combine like terms: $72x - 72 + 8x^2 - 8x = 72x$ .
Subtract $72x$ : Subtract $72x$ from both sides to get: $8x^2 - 8x - 72 = 0$ .
Divide by $8$ : Divide the entire equation by $8$ to simplify: $x^2 - x - 9 = 0$ .

More problems from Identify quotients of rational numbers: word problems

Question

\frac{x}{x+3} = \frac{x+2}{x+6.2}

Posted 3 months ago

Question

The least amount of wrapping paper needed to wrap a cube-shaped gift is

150

square inches. How long is one side of the gift?

Posted 2 months ago

Question

Which expression is equivalent to

30.4+(-40.4)

\newline

30.4-40.4

\newline

40.4-30.4

\newline

-40.4+(-30.4)

\newline

-40.4-30.4

Posted 2 months ago

Question

n

and simplify your answer.

\newline

-6=\frac{2}{3} n

\newline

Posted 2 months ago

Question

3+2.5\times 5-4\times 8=

Posted 3 months ago

Question

A local package delivery service wants to improve the efficiency of its deliveries. As a first step, the management team decides to conduct a study to determine the average length of time from the arrival of a package at the company's mail center until its delivery at a home. Which of the following methods is most likely to produce valid results?

\newline

1

\newline

(A) The team selects the

1,000

heaviest packages in a one-week, non-holiday period and records how long it takes for each package to reach its destination.

\newline

(B) The team calls

1,000

residents in their delivery area and asks them whether they have received a package from their service in the past week. They will then record how long it took for those packages to reach their destination.

\newline

(C) The team selects a random sample of

1,000

packages arriving at the center over a one-week, non-holiday period and records how long it takes for each package to reach its destination.

\newline

(D) None of the above

Posted 3 months ago

Question

8+2.7=

Posted 3 months ago

Question

(1.5-2.9 i)+(4.3+1.4 i)

Posted 3 months ago

Question

3

(c)

of flour to bake

2

loaves of bread. If

1

(lb)

of flour is equivalent to

3\frac{1}{3} c ,

how many loaves of bread can the baker make with a

10

lb

- bag of flour?

\newline

(Round the answer to the nearest whole number.)

\newline

\square

Posted 3 months ago

Question

\newline

-0.1 \times \frac{-2}{5}=

Posted 3 months ago