Question

Sarah runs a day camp in the summer and needs to buy paper towels and soap for the restrooms. She spends $129 on t cases of paper towels and s cases of soap. Each case of paper towels is $12 and contains 10 rolls of paper towels. Each case of soap is $15 and contains 12 bottles of soap. Sarah buys 10 cases of supplies altogether.
Part A- Write a system of two equations to represent the cases of supplies Sarah buys. Explain your work.

Part B. How many cases of paper towels did Sarah buy? Show or explain your work.

Part C- Explain why it would not be possible for Sarah to buy exactly 20 bottles of soap.


please answer all parts and show work

Thank you

Answer 1

Let x be the number of cases of paper towels and y be the number of cases of soap. The system of linear equation that would best represent the given is,
                                 x + y = 10
                               12x + 15y = 129
The values of x and y are 7 and 3. 

Sarah both 7 cases of paper towel.

It is not possible for Sarah to buy exactly 20 bottles because first of all the cases contains only 12 bottles and 20 is not divisible by 12.