Chapter 9.5, Problem 9P

To determine

To find: The bill for a glass of juice and a salad.

Answer to Problem 9P

The bill of a glass of juice and a salad is $2.20$ .

Explanation of Solution

Given information:

The given five glass of apple juice and four salads is $9.50$ .

Apple juice and five salads is 10.30.

Calculation:

The cost price of a glass of juice be $x$ and salad be $y$ .

Bill for five glasses of juice and four salads is $9.50$ .

  $5x+4y=\mathrm{9.50................}\left(1\right)$ .

Bill for four glasses of juice and five salads is $10.30$

  $4x+5y=\mathrm{10.30..........}\left(2\right)$

Multiply equation $\left(1\right)$ by $5$ .

  $\begin{array}{l}5\left(5x+4y\right)=5\left(9.50\right)\\ 25x+20y=\mathrm{47.5.................}\left(3\right)\end{array}$

Multiply equation $\left(2\right)$ by $4$ .

  $\begin{array}{l}4\left(4x+5y\right)=4\left(10.30\right)\\ 16x+20y=\mathrm{41.2..............}\left(4\right)\end{array}$

Subtract equation $\left(4\right)$ from equation $\left(3\right)$ .

  $\begin{array}{c}25x+20y=47.5\\ 16x+20y=41.2\\ 9x=6.3\\ x=0.7\end{array}$

Substitute the value of $x$ in $\left(1\right)$ .

  $\begin{array}{c}5x+4y=9.50\\ 3.50+4y=9.50\\ y=1.50\end{array}$

The cost price of glass of juice is 0.7 .

The cost price of a salad is 1.50.

Therefore, the bill of a glass of juice and a salad is $2.20$ .