Find the cost of each item.

Question

a store sells​ tents, sleeping​ bags, and camp stools. A customer buys a​ tent, 4 sleeping​ bags, and 3 camp stools for ​$281. The price of the tent is 6 times the cost of a camp stool. The cost of a sleeping bag is $41 more than the cost of a camp stool.

Answer 1

Let T be the price of a tent, S be the price of a sleeping bag, and C the price of a camp stool.

We are given that T + 4S + 3C = 281.

Also T = 6C and S = C + 41.

Substituting

6C + 4 (C + 41) + 3C =281

or

13 C + 164 = 281

or 13 C = 117

Knowing the value of C, we can use the given information to find the values of T and S.

Answer 2

t = price of a tent

b = price of a sleeping bag

c = price of a camp stool

t + 4b + 3c = 281

t = 6c

b = c + 41

We created a system of linear equation from above. Use the substitution method to solve for the variables.

6c + 4(c + 41) + 3c = 281

6c + 4c + 164 + 3c = 281

13c + 164 = 281

13c = 117

c = 9

b = 9 + 41

b = 50

t = 6(9)

t = 54

Check: 54 + 4(50) + 3(9) = 54 + 200 + 27 = 200 + 81 = 281

The price of a tent costs $9. The price of a sleeping bag costs $50. The price of a camp stool costs $54.