Donating money to charities

Algebra Level 2

A student wishing to give $25$ cents to each of several charities finds that he is $10$ cents short. If, instead, he gives $20$ cents to each of the charities, then he is left with $25$ cents. Find the amount of money with which the student starts. Give your answer in cents.

The answer is 165.

1 solution

A Former Brilliant Member
Apr 24, 2017

$x$ = amount of money with which the students starts in cents

$n$ = number of charities

The first condition translated, becomes

$x-25n=-10$ $\color{#D61F06}(1)$

The second condition translated, becomes

$x-20n=25$ $\color{#D61F06}(2)$

Subtracting $\color{#D61F06}(1)$ from $\color{#D61F06}(2)$ , we obtain

$5n=35$

Dividing both sides by $5$ , we get

$n=7$

Finally,

$x-25n=-10$

$x-25(7)=-10$

$\large\color{#3D99F6}\boxed{x=165~cents}$ $\large\color{#20A900}\boxed{\text{answer}}$

Donating money to charities

The answer is 165.

1 solution

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