Question

Use pictures and equations to show your work.At the end of the year, Mrs. Weeks bought an assortment of new balls toreplace some of the old ones. She had $150.00 to spend. Describe twodifferent ways that Mrs. Weeks could spend her money if she bought at leasttwo of each of the balls.Use coins or cut out the manipulatives on the next page to help you act outthe problem.

Answer 1

First, let's calculate the amount of money required to purchase two of each type of ball:

`\begin{gathered} C=2(8+9+7+5)\\ \\ C=2\cdot29\\ \\ C=58 \end{gathered}`

Now, to complete the remaining amount of money, we can choose more balls until the total cost reaches $150.

For example, let's add two more of each type of ball. So the total cost will be 116.

Then, to complete the remaining $34, let's create two possibilities of adding more balls:

- 2 baseballs and 4 softballs

- 3 basketballs and 1 baseball

Therefore two possibilities are:

4 footballs, 4 basketballs, 6 baseballs and 8 softballs;

4 footballs, 7 basketballs, 5 baseballs and 4 softballs.

Let's check if the total cost of each case is $150:

`\begin{gathered} C_1=4\cdot8+4\cdot9+6\cdot7+8\cdot5=32+36+42+40=150\\ \\ C_2=4\cdot8+7\cdot9+5\cdot7+4\cdot5=32+63+35+20=150 \end{gathered}`