Chapter 6.4, Problem 37PFA

a.

To determine

To define the variables and to write the system of linear equations

Answer to Problem 37PFA

System of equations:

  $\begin{array}{l}9x+12y=1845\\ 8x+15y=2127.50\end{array}$

Explanation of Solution

Given:

The table shows the number of cartons of cookies and candy bars sold by each team with the money collected.

Calculation:

Let x be the money collected from selling one cartons of cookies and y be the money collected from selling one cartons of Candy Bars.

The money collected by selling cartons of cookies and candy bars sold by football team is represented as

  $\Rightarrow 9x+12y=\mathrm{1845.................}(1)$

The money collected by selling cartons of cookies and candy bars sold by Track team is represented as

  $\Rightarrow 8x+15y=\mathrm{2127.50..................}(2)$

Conclusion:

Therefore, the equations are $9x+12y=1845$ and $8x+15y=\mathrm{2127.50.}$

b.

To determine

To find the solution of the system of equations found in subpart (a).

Answer to Problem 37PFA

Cookies: $55

Candy bars: $112.5

Explanation of Solution

Given:

From subpart (a),

System of equations:

  $9x+12y=1845$

  $8x+15y=2127.50$

Calculation:

Let x be the money collected from selling one cartons of cookies and y be the money collected from selling one cartons of Candy Bars.

Multiply equation (1) with 8,

  $\Rightarrow 72x+96y=14760$

Multiply equation (2) with 9,

  $\Rightarrow 72x+135y=19147.50$

Subtracting the above equations,

  $\begin{array}{l}\Rightarrow (72x+135y)-(72x+96y)=19147.50-14760\\ \Rightarrow 135y-96y=4387.50\\ \Rightarrow 39y=4387.50\\ \Rightarrow y=112.5\end{array}$

Substitute the value of y in $8x+15y=2127.50$ ,

  $\begin{array}{l}\Rightarrow 8x+15(112.5)=2127.50\\ \Rightarrow 8x+1687.5=2127.50\\ \Rightarrow 8x=440\\ \Rightarrow x=55\end{array}$

Conclusion:

Therefore, the price of one carton of cookies is $55 and the price of candy bars is $112.5

c.

To determine

To find the selling price of one box of cookies and candy bars.

Answer to Problem 37PFA

One box cookies: $5.5

One candy bar: $2.25

Explanation of Solution

Given:

Number of boxes in one carton of cookies: 10

Number of boxes in one carton of candy bars: 50

Calculation:

From subpart (b),

The price of one carton of cookies is $55

So, one carton has 10 boxes of cookies.

The price of one box of cookies is,

  $\Rightarrow \frac{55}{10}=\$5.5$

The price of one carton of candy bars is $112.5

So, one carton has 50 candy bars.

The price of one candy bar is,

  $\Rightarrow \frac{112.5}{50}=\$2.25$

Conclusion:

Therefore, price of one box cookies is $5.5 and one candy bar is $2.25