SOLUTION: Whitney has 20 coins in her purse. Some are quarters and some are dimes. The total value of the coins is $3.35. How many quarters does Whitney have?

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Question 1171403: Whitney has 20 coins in her purse. Some are quarters and some are dimes. The total value of the coins is $3.35. How many quarters does Whitney have?



Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

x quarters

20-x dimes


Total money equation

    25x + 10*(20-x) = 335  cents.


It implies

    25x + 200 - 10x = 335

    25x - 10x       = 335 - 300

       15x          = 135

         x          = 135/15 = 9.


ANSWER.  9 quarters and 20-9 = 11 dimes.


CHECK.   9*25 + 11*10 = 335  cents, in total.   ! Correct !

Solved.



Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


A quick mental solution method, if formal algebra is not required....

(1) Imagine 20 coins that are all dimes; the value would be $2.00, which is $1.35 less than the actual total.
(2) Now imagine switching dimes for quarters, one at a time. Each time, the number of coins stays the same, while the value of the coins increases by 25-10 = 15 cents.
(3) The number of times you need to do that to make up the additional $1.35 (135 cents) is 135/15 = 9.
(4) Therefore, 9 of the coins are quarters.

ANSWER: 9 quarters (and 11 dimes)

CHECK: 9(25)+11(10) = 225+110 = 335
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