A man has 34 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 565 cents, how many dimes and how many quarters does he have?

Question

Genesis Allen · Accepted Answer

#19# dimes and #15# quarters.

#34=x+y# #34-x=y# #565=10x+25y# Substitute the first equation, so #565=10x+25(34-x)# #565=10x+850-25x# #15x=285# #x = "19 dimes"# Therefore #34-19 = "15 quarters"#

Ethan Adkins · Answer

undefined Let $ d $ represent the number of dimes and $ q $ represent the number of quarters.

We have two equations based on the given information:

1. The total number of coins: $ d + q = 34 $
2. The total value of the coins: $ 10d + 25q = 565 $

We can use these equations to solve for $ d $ and $ q $ simultaneously.

From the first equation, we can express $ q $ in terms of $ d $:

$ q = 34 - d $

Substitute this expression for $ q $ into the second equation:

$ 10d + 25(34 - d) = 565 $

Now, solve for $ d $:

$ 10d + 850 - 25d = 565 $

$ -15d = -285 $

$ d = 19 $

Now that we have found $ d $, we can substitute it back into the first equation to find $ q $:

$ q = 34 - 19 $

$ q = 15 $

So, the man has 19 dimes and 15 quarters.