Question

Last year, a property manager bought five identical snow shovels and six identical bags of salt. the total of the snow shovels was 172.50 before tax and each bag of salt cost 6.20$ before tax.

This year the property manager bought two identical snow shovels and four identical bags of salt. the total cost of snow shovels was 70.38$ before tax and the total cost of the bags of salt was 26.04$ before tax.

Determine the item with the greatest percent increase in the price from last year to this year. Be sure to include the percent increase of this item to the nearest percent.

(Explain your answer)

Answer 1

The salt had a greater percent of increase, 5%.

Explanation:

Last year, 5 shovels cost $172.50 before tax. This means each shovel cost

172.50/5 = 34.50

We are told that each bag of salt cost $6.20 last year.

This year, 2 shovels cost $70.38 before tax. This means each shovel costs

70.38/2 = 35.19

4 bags of salt cost $26.04 before tax. This means each bag of salt costs

26.04/4 = 6.51

To find the percent increase, we use the ratio

`\frac{\text{amount of change}}{\text{original amount}}`

The amount of change for the shovels was

35.19-34.50 = 0.69

This means the percent increase will be

0.69/34.50 = 0.02 = 2%

The amount of change for the bags of salt was

6.51-6.20 = 0.31

This means the percent increase will be

0.31/6.20 = 0.05 = 5%

The salt has a larger percent of increase, 5%.

Answer 2

Just compare the change in unit cost to the original unit cost.

Shovels: (70.38 ÷ 2 - (172.50/5) ÷ (172.50/5) = 0.02
Salt: (26.04 ÷ 4 - (6.20) ÷ 6.20 = 0.05

So, the shovels went up 2% and the salt went up 5%