Q38. - Algebra 1

Question

MONEY Chris has saved twice the number of quarters that Nora saved plus 6. The number of quarters Chris saved is also five times the difference of the number of quarters and 3 that Nora has saved. Write and solve an equation to find the number of quarters they each have saved.

Step-by-Step Solution

Answer

The number of quarters saved by Nora and Chris are 7 and 20 respectively.

Step 1. List the given data.

Chris has saved twice the number of quarters that Nora saved plus 6.

 

The number of quarters Chris saved is also five times the difference of the number of quarters and 3 that Nora has saved.

Step 2. Formulate the equation.

Let the number of quarters saved by Nora be x.

 

Since Chris has saved twice the number of quarters that Nora saved plus 6, the number of quarters saved by Chris is $2x+6$.

 

It is given that the number of quarters Chris saved is also five times the difference of the number of quarters and 3 that Nora has saved.

 

Translating the given condition into an equation,

 

$2x+6=5\left(x-3\right)$

Step 3. Solve the obtained equation.

Solving,

$2x+6=5\left(x-3\right)$  (Given equation)

$2x+6=5x-15$  (Distributive property)

$2x+6-5x=5x-15-5x$  (Subtract $5x$ from both sides)

$-3x+6=-15$  (Simplify)

$-3x+6-6=-15-6$  (Subtract 6 from both sides)

$-3x=-21$  (Simplify)

$\frac{-3x}{-3}=\frac{-21}{-3}$  (Divide both sides by $-3$)

$x=7$  (Simplify)

So, $x=7$ is the solution of the given equation.

Step 4. Interpret the obtained solution.

It was assumed that the number of quarters saved by Nora is $x$ and the number of quarters saved by Chris is $2x+6$.

 

It was obtained that for the given condition to be satisfied, $x=7$.

 

Put $x=7$ in $2x+6$ to get,

$\begin{array}{c}2x+6=2\left(7\right)+6\\ =14+6\\ =20\end{array}$

So, $2x+6=20$.

 

Then, the number of quarters saved by Nora and Chris are 7 and 20 respectively.