Question

Mrs. Mahoney went shopping for some canned goods which were on sale. She bought three times as many cans of tomatoes as cans of peaches and two times as many cans of tuna as cans of peaches. If Mrs. Mahoney purchased a total of 24 cans, how many of each did she buy? Please be descriptive and show steps.

Answer 1

Let t, p and tuna be the quanity of tomatoes, peaches and tuna respectively. Solve the following equations for t, p and tuna.\[\left\{\frac{t}{p}=3,\frac{\text{tuna}}{p}=2,t+p+\text{tuna}=24\right\}\]\[\{t=12,p=4,\text{tuna}=8\} \]

Answer 2

So can you show me the steps to get t = 12, p = 4, and tuna = 8?

Answer 3

Let p = number of cans of peaches she bought
Then 2p = number of cans of tuna
And 3p = number of cans of tomatoes.

Add them all up and we should get 24 cans:
p+2p+3p=24
Add the like terms
6p=24
Divide both sides by 6
p=4 cans of peaches
2p=2(4)=8= cans of tuna
3p=3(4)=12 cans of tomatoes

Answer 4

"She bought three times as many cans of tomatoes as cans of peaches and two times as many cans of tuna as cans of peaches." That is the sentence that confuses me the most.

Answer 5

@Albert0898
Can you solve the following equations for p and tuna?\[\left\{\frac{\text{tuna}}{p}=2,3p+p+\text{tuna}=24\right\}\]