Question

Last year, a property manager bought five identical snow shovels and six identical bags of salt. The total cost 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 the 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 rice from last year to this year. Be sure to include to the precent increase of this item to the nearest percent.

Answer 1

Let h be the number of shovels.
5h = 172.50 (5 shovels totaled $172.50)
Divide both sides by 5:
5h/5 = 172.50/5
h = 34.50
Last year, each shovel was $34.50.
Each bag of salt last year was $6.20.

This year:
2h = 70.38 (2 shovels totaled $70.38)
Divide each side by 2:
2h/2 = 70.38/2
h = 35.19

Let a be the cost of a bag of salt.
4a = 26.04 (4 bags of salt totaled $26.04)
Divide both sides by 4:
4a/4 = 26.04/4
a = 6.51
This year, shovels cost $35.19 each and bags of salt cost $6.51 each.
To find the percent increase in shovels, first find the amount of increase:
35.19 (this year) - 34.50 (last year) = 0.69 increase
Divide the amount of increase by the original amount:
0.69/34.50 = 0.02
There was a 2% increase in shovel costs.
To find the percent increase in salt, first find the amount of increase:
6.51 (this year) - 6.20 (last year) = 0.31 increase
Divide the amount of increase by the original amount:
0.31/6.20 = 0.05
There was a 5% increase in salt costs. The salt had a higher percent of increase.