Answer:
The variables are P for pennies and Q for quarters, and solving the equations we can find that they have 9 quarters and 27 pennies.
Step-by-step explanation:
We know that they have quarters and pennies, then the variables that we will use are:
P = total number of pennies
Q = total number of quarters.
Now let's solve the problem.
We know that the value of a penny is $0.01
We know that the value of a quarter is $0.25
We know that he has 22 coins, and she has 14 coins.
Then the total number of coins is 22 + 14 = 36 coins, then:
P + Q = 36
We also know that the total value of these coins is $2.52
then:
P*$0.01 + Q*$0.25 = $2.52
Then we have a system of equations:
P + Q = 36
P*$0.01 + Q*$0.25 = $2.52
To solve it, we need to start by isolate one of the variables in one of the equations, let's isolate P in the first one
P = 36 - Q
Now we can replace this in the other equation:
(36 - Q)*$0.01 + Q*$0.25 = $2.52
Now we can solve this for Q.
36*$0.01 - Q*$0.01 + Q*$0.25 = $2.52
$0.36 + Q*$0.24 = $2.52
Q*$0.24 = $2.52 - $0.36 = $2.16
Q = $2.16/$0.24 = 9
Then they have 9 quarters, and the number of pennies is given by
P = 36 - Q = 36 - 9 = 27
They have 27 pennies.
