Chapter 3, Problem 48SGR

To determine

The cost of 1 pound of nuts and 1 pound of raisins.

Answer to Problem 48SGR

The cost of 1 pound of nuts is $5.25 and the cost of 1 pound of raisins is $6.5

Explanation of Solution

Given:

Sonia bought 2 pounds of nuts and 2 pounds of raisins for $23.50 and Drew bought 3 pounds of nuts and 1 pound of raisins for $22.25.

Calculation:

Let the cost of 1 pound of nuts be $x and the cost of 1 pound of raisins be $y.

Now total money spent by Sonia is,

  $2x+2y=23.50\to \left(1\right)$

The total money spent by Drew is,

  $3x+y=22.25\to \left(2\right)$

Now multiplying equation (2) by 2 and subtracting equation (1) from it, we get

  $\begin{array}{l}2\left(3x+y\right)-\left(2x+2y\right)=2\left(22.25\right)-23.50\\ \Rightarrow 4x=21\\ \Rightarrow x=5.25\end{array}$

Now put $x=5.25$ in equation (2), we get

  $\begin{array}{l}3\left(5.25\right)+y=22.25\\ \Rightarrow 15.75+y=22.25\\ \Rightarrow y=6.5\end{array}$

Hence the cost of 1 pound of nuts is $5.25 and the cost of 1 pound of raisins is $6.5