Chapter 4.1, Problem 70STP

To determine

To Find:

How many cans each did the 10^th and 12^th grade classes collect? Show your work.

Answer to Problem 70STP

10^th = 275; 12^th = 330

Explanation of Solution

Given Information :

The table shows the results of a canned food drive.1225 cans were collected, and the 12^th grade class collected 55 more cans than the 10^th grade class.

  

Calculation:

Number of cans collected by 10^th and 12^th grade :

  $\begin{array}{l}340+x+280+y=\mathrm{1225....................}[given\_total\_cans\_collected=1225]\\ \Rightarrow 620+x+y=\mathrm{1225.........................}[simplify]\\ \Rightarrow 620+x+y-620=1225-\mathrm{620.....}[subtract"620"each\_side]\\ \Rightarrow x+y=\mathrm{605....................................}(1)\end{array}$

Also ,

12^th grade class collected 55 more cans than the 10^th grade class.

  $\Rightarrow y=x+55$

So,

  $\begin{array}{l}10th=x\\ 12th=x+55\end{array}$

Putting is equation (1) :

  $\begin{array}{l}x+y=\mathrm{605.............................}(1)\\ \Rightarrow x+(x+55)=605\\ \Rightarrow 2x+55=605\\ \Rightarrow 2x+55-55=605-\mathrm{55........}[subtract"55"each\_side]\\ \Rightarrow 2x=\mathrm{550..............................}[simplify]\\ \Rightarrow \frac{2x}{2}=\frac{550}{2}\mathrm{.............................}[divide"2"each\_side]\\ \Rightarrow x=275\\ \Rightarrow y=x+55=275+55=330\end{array}$

So,

10^th = 275

12^th = 330