Chapter 6.5, Problem 19PPS

a.

To determine

To define the variables and write the system of equations

Answer to Problem 19PPS

  $\begin{array}{l}9x+26y=3.77\\ 9x+114y=4.65\end{array}$

Explanation of Solution

Given:

Amount that Mara earned is $3.77

Amount that Ling earned is $4.65

Let x be the cost of one pound of Aluminium cans and y be the cost of one pound of newspaper.

From the table, the number of Aluminium cans and newspaper that Mara and Ling recycled is,

  $\begin{array}{l}\Rightarrow 9x+26y=\mathrm{3.77.................}(1)\\ \Rightarrow 9x+114y=\mathrm{4.65...............}(2)\end{array}$

Conclusion:

Therefore, the system of equations are $9x+26y=3.77$ and $9x+114y=\mathrm{4.65.}$

b.

To determine

To find the cost of one pound of Aluminium

Answer to Problem 19PPS

$0.39

Explanation of Solution

Given:

From subpart (a),

  $\begin{array}{l}9x+26y=3.77\\ 9x+114y=4.65\end{array}$

Calculation:

  $\begin{array}{l}\Rightarrow 9x+26y=\mathrm{3.77.................}(1)\\ \Rightarrow 9x+114y=\mathrm{4.65...............}(2)\end{array}$

Subtracting equation (1) from equation (2),

  $\begin{array}{l}\Rightarrow (9x+114y)-(9x+26y)=4.65-3.77\\ \Rightarrow 114y-26y=0.88\\ \Rightarrow 88y=0.88\\ \Rightarrow y=0.01\end{array}$

Substitute the value of y in equation (1),

  $\begin{array}{l}\Rightarrow 9x+26(0.01)=3.77\\ \Rightarrow 9x+0.26=3.77\\ \Rightarrow 9x=3.51\\ \Rightarrow x=0.39\end{array}$

Conclusion:

Therefore, the cost of one pound of Aluminium can is $0.39.