Question

A store sells​ tents, sleeping​ bags, and camp stools. A customer buys a​ tent, 3 sleeping​ bags, and 4 camp stools for ​$170. The price of the tent is 9 times the cost of a camp stool. The cost of a sleeping bag is ​$30 more than the cost of a camp stool. Find the cost of each item.

Answer 1

Answer: the cost of a tent is $45

the cost of a sleeping bag is $35

the cost of a camp stool is $5

Step-by-step explanation:

Let x represent the cost of a tent.

Let y represent the cost of a sleeping bag.

Let z represent the cost of a camp stool.

A customer buys a​ tent, 3 sleeping​ bags, and 4 camp stools for ​$170. It means that

x + 3y + 4z = 170- - - - - - - - - - - - - - -1

The price of the tent is 9 times the cost of a camp stool. It means that

x = 9z

The cost of a sleeping bag is ​$30 more than the cost of a camp stool. It means that

y = z + 30

Substituting x = 9z and y = z + 30 into equation 1, it becomes

9z + 3(z + 30) + 4z = 170

9z + 3z + 90 + 4z = 170

9z + 3z + 4z = 170 - 90

16z = 80

z = 80/16

z = 5

y = z + 30 = 5 + 30

y = 35

x = 9z = 9 × 5

x = 45

Answer 2

Answer:

Cost of camp stool is $5 , cost of tent is $45 and cost of sleeping bag is $35

Step-by-step explanation:

Customer buys 1 tent,3 sleeping bags and 4 camp stools.

Let the cost of the camp stool = $\[x\]$

Then the price of the tent = $\[9*x\]$

Cost of the sleeping bag = $\[x+30\]$

The total cost of the items purchased by him is $170

$\[=> 9x + 4x + 3(x+30) = 170\]$

$\[=> 9x + 4x + 3x+90 = 170\]$

$\[=> 16x = 80\]$

$\[=> x = 5\]$

So cost of camp stool is $5 , cost of tent is $45 and cost of sleeping bag is $35.