Question

A man has 16 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.50, how many dimes and how many quarters does he have?

Let d = number of dimes, q = number of quarters.

Step one:

A man has 16 coins in his pocket, all of which are dimes and quarters.

Set up the first equation for the number of dimes and quarters. Help PLS

Answer 1

Answer: 10 dimes and 6 quarters, see below for the equations.

Explanation:

We know how much a dime is worth and how much a quarter is worth, and they give us the total number of coins and the total number of change.

This equation shows the total number of coins:

d + q = 16

This equation shows the worth of these coins:

0.10d + 0.25q = 2.5

Now, we can graph these equations. See attached. The point of intersection, where the lines cross, is our solution. In the graph, d = x and q = y.

This point is (10, 6) meaning he has 10 dimes and 6 quarters in his pocket.