We want to write and solve a system of equations to see how many coins of each type Mary has. We will find that there are 28 nickels and 14 quarters.
Let's start by defining the variables:
- q = number of quarters
- n = number of nickels.
We know that she has 42 coins, then:
q + n = 42
We also know the total value of the coins, remember that the value of one quarter is $0.25 and the value of one nickel is $0.05, then we can write:
q*$0.25 + n*$0.05 = $4.90
So the system of equations is:
q*$0.25 + n*$0.05 = $4.90
q + n = 42
To solve this, we need to isolate one of the variables in one of the equations, I will isolate q in the second one:
q = 42 - n
Replacing that in the other equation we get:
(42 - n)*$0.25 + n*$0.05 = $4.90
$10.50 - n*$0.20 = $4.90
$10.50 - $4.90 = n*$0.20
$5.60 = n*$0.20
$5.60/$0.20 = n = 28
So there are 28 nickels, and the other 14 coins are quarters.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/9351049
