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A certain store sells only jacks and marbles. A single jack costs...

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by swerve » Sat Jan 18, 2020 2:36 pm
A certain store sells only jacks and marbles. A single jack costs 19 cents and a single marble costs 25 cents. In how many different ways can one spend exactly $10 buying items at this store?

A. 0
B. 1
C. 2
D. 3
E. 4

The OA is D


Source: Veritas Prep
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Re: A certain store sells only jacks and marbles. A single jack costs...

by Jay@ManhattanReview » Mon Jan 20, 2020 9:33 pm
swerve wrote: ↑
Sat Jan 18, 2020 2:36 pm
 A certain store sells only jacks and marbles. A single jack costs 19 cents and a single marble costs 25 cents. In how many different ways can one spend exactly $10 buying items at this store?

A. 0
B. 1
C. 2
D. 3
E. 4

The OA is D

Source: Veritas Prep
Say one bought x jacks and y marbles, where x and y are nonnegative integers.

Thus, 19x + 25y = 1,000

=> x = (1,000 – 25y)/19 = 25*[(40 – y)/19];

Since x is a non-negative integer, (40 – y)/19 must be a non-negative integer, too.

Possible values of y are 40, 21 and 2; thus the corresponding values of x are 0, 25 and 50. There are three ways.

The correct answer: D

Hope this helps!

-Jay
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