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a man has 23 coins in his pocket, all of which are dimes and quarters. if the total value of his change is 380 cents, how many dimes and how many quarters does he have? your answer is



Answer :

We found that after simplifying , He have 13 dimes and 10 quarters.

Given,

A man has 23 coins in his pocket.

The total value of his change is 380 cents.

Now,

23 = x + y

23 - x = y

As we know that

A dime=10 cents

So the cost of x dime is 10x.

A quarter=25 cents

so the cost of y quarters is 25y.

380 = 10x + 25y

Substitute the first equation, so

389 = 10x + 25 (23 - x)

380 = 10x + 575 - 25x

15x = 195

x = 13 dimes

Therefore,

y = 23 - 13 = 10 quarters

y = 10 quarters

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