Q. 352 - Intermediate Algebra

Question

Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and calculator. Troy bought four notebooks and five calculators for$\backslash (116$. Lisa

bought two notebooks and three calculators for$\backslash )68$. Find the cost of each notebook and each thumb drive.

Step-by-Step Solution

Answer

The cost of each notebook is$\$4$

The cost of each thumb drive is$\$20$

Step 1. Given information

Troy bought four notebooks and five thumb drives  for$\$116$.

Lisa bought two notebooks and three thumb drives  for$\$68$.

Step 2. Forming two linear equations using two given conditions.

Let $x$ be the cost of notebook.

Let $y$ be the cost of thumb drive.

Using Troy condition, we get eq.(i) as

$4x+5y=116$

Using Lisa condition, we get eq.(ii) as

$2x+3y=68$

Step 3. Find value of x and y by solving linear equations using substitution method

Using eq.(i), find $x$

$$\begin{gathered} 4x+5y=116 \\ x=\frac{116-5y}{4} \end{gathered}$$

Substitute this value of $x$ in eq.(ii),

$$\begin{gathered} 2x+3y=68 \\ 2\left(\frac{116-5y}{4}\right)+3y=68 \\ 58-\frac{5y}{2}+3y=68 \\ \frac{y}{2}=10 \\ y=20 \end{gathered}$$

Now substitute this value of $y$ in any of the equation,

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

Step 4. Check by substituting values in both the equations

Substitute $x=4,y=20$ in both the equations

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

This is true

$$\begin{gathered} 2x+3y=68 \\ 2\left(4\right)+3\left(20\right)=68 \\ 8+60=68 \\ 68=68 \end{gathered}$$

This is also true

Step 5. Required answer

The cost of each notebook is $\$4$

The cost of each thumb drive is $\$20$