Question

During two years in college, a student earned \(9,500. The second year she earned \)500 more than twice the amount she earned the first year. How much did she earn the first year?

Short answer

The amount earned in first year = $3000

The amount earned in second year=$6500

Step-by-step solution

Given Information 

During two years in college, a student earned $9,500. The second year she earned $500 more than twice the amount she earned the first year.

Assume variables and frame equations

Let 'x' be the amount earned in first year

and 'y' be the amount earned in second year

During two years in college, a student earned $9,500.

x + y=9500

The second year she earned $500 more than twice the amount she earned the first year.

y=2x+500

solve both the equations

$$\begin{gathered} x+y=9500 \\ y=2x+500 \\ Substituteyinfirstequaion \\ x+y=9500 \\ x+2x+500=9500 \\ 3x+500=9500 \\ 3x=9500-500 \\ 3x=9000 \\ divideby3 \\ x=3000 \\ y=2x+500 \\ y=2\left(3000\right)+500 \\ y=6500 \end{gathered}$$

The amount earned in first year = $3000

The amount earned in second year=$6500