### Home > AC > Chapter 8 > Lesson 8.3.3 > Problem8-116

8-116.

Write and solve an equation (or system of equations) for the situation described below. Define your variable(s) and write your solution as a sentence.

Daria has $18$ coins that are all nickels and quarters. The number of nickels is $3$ more than twice the number of quarters. If she has $\1.90$ in all, how many nickels does Daria have?

$n=$ # of nickels
$q=$ # of quarters

Use the information in the problem to set up a system of equations.

$2q+3=n$

$0.05n + 0.25q = 1.9$

Substitute $2q+3$ in for $n$.

$0.05(2q + 3) + 0.25q = 1.9$

Solve for $q$.

$0.1q + 0.15 + 0.25q = 1.9$

$0.35q = 1.75$

$q=5$

Substitute $5$ into one of the original equations for $q$.

$2(5) + 3 = n$

$10+3=n$

$13=n$