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a group of parents decided to buy paying in equal parts an encyclopedia to donate to the neighborhood school the price of

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A group of parents decided to buy, paying in equal parts, an encyclopedia to donate to the neighborhood school, the price of which is $400. If the number of parents contributing to the purchase increased by a quarter, each one would pay $ 1 less. How many are the parents? How much does each one contribute?

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Answer to a math question A group of parents decided to buy, paying in equal parts, an encyclopedia to donate to the neighborhood school, the price of which is $400. If the number of parents contributing to the purchase increased by a quarter, each one would pay $ 1 less. How many are the parents? How much does each one contribute?

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114 Answers

Let the original number of parents be

x

and each parent contributes

y

dollars.
Thus, the total cost of the encyclopedia can be expressed as

xy = 400

.

According to the second condition, if the number of parents increases by a quarter, the new number of parents becomes

\frac{5}{4}x

.
Also, the new contribution per parent is

y-1

.

Thus, the new total cost can be expressed as

\left(\frac{5}{4}x\right)(y-1) = 400

.

We now have the system of equations:

xy = 400

\left(\frac{5}{4}x\right)(y-1)=\frac{5}{4}xy-\frac{5}{4}x=400

Substituting the first expression into the second gives us the following:

\frac{5}{4}(400)-\frac{5}{4}x=400

500-\frac{5}{4}x=400

100=\frac{5}{4}x

Solving the equation above, we find

x=100\cdot\frac{4}{5}=80

and

y=5

, meaning there are originally 80 parents and each contributes $5.

\textbf{Answer:}

There are 80 parents and each one contributes $5.

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