Write a system of equation based on the problem
A quarter is worth $0.25 and a nickle is worth $0.05. Suppose the number of quarters is represented by q and the number of nickels is represented by n.
First Equation
"There are 7 more quarters than nickels" could be written as
⇒ q = n + 7
Second Equation
"There is a total of $2.65" could be written as
⇒ 0.25q + 0.05n = 2.65 (change to whole number, multiply both side by 100)
⇒ 25q + 5n = 265
Work on the system of equation
Substitute q = n + 7 to the second equation
25q + 5n = 265
25(n + 7) + 5n = 265
25n + 175 + 5n = 265
30n + 175 = 265
30n = 265 - 175
30n = 90
n = 90/30
n = 3
The number of nickels is 3
Substitute n = 3 to the first equation
q = n + 7
q = 3 + 7
q = 10
The number of quarters is 10
