Question

In the following exercises, translate to a system of equations and solve.

Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive.Troy bought four notebooks and five thumb drives for \(116. Lisa bought two notebooks and three thumb dives for \)68. Find the cost of each notebook and each thumb drive

Short answer

The cost of notebook is $4 and cost of thumbdrive is $20

Step-by-step solution

Step 1. Given Information   

The given data is that Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive.Troy bought four notebooks and five thumb drives for $116. Lisa bought two notebooks and three thumb drives for $68.

Step 2. Explanation   

Let the cost of notebook be x and cost of thumbdrive be y.

The cost of four notebooks and five thumb drives is $116 that is $4x+5y=116--\left(1\right)$

The cost of two notebooks and three thumb drives is $68 that is$2x+3y=68--\left(2\right)$

Step 3. Calculation  

Rewrite the equation (2) by multiplying it with 2.

$$\begin{gathered} 2(2x+3y)=2\left(68\right) \\ 4x+6y=136--\left(3\right) \end{gathered}$$

Solve the equation (1) and (3) by subtracting equation (1) from equation (3).

$$\begin{gathered} 4x+6y-4x-5y=136-116 \\ y=20 \end{gathered}$$

Substitute the value of y in equation (1) and simplify.

$$\begin{gathered} 4x+5\left(20\right)=116 \\ 4x+100=116 \\ 4x=16 \\ x=4 \end{gathered}$$