Question

A company that offers tubing trips down a river rents tubes for a person to use and “cooler” tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. Use x to represent the number of one-person tubes rented and y to represent the number of cooler tubes rented. a one person tube costs $20 and a cooler tube costs $12.50 How many of each type of tube does the group rent? what are the two system of equations?

Answer 1

Answer:- 1)The group rents 11 person tubes and 4 cooler tubes.

2) The two system of equations are

x+y=15

20x+12.50y=270

Explanation:-

Given: x represents the number of person tubes rented and y represents the number of cooler tubes rented such that

$x+y=15$

⇒$y=15-x$.........(1)

Cost of a person tube=$20

Cost of a cooler tube=$12.50

Total spending on tube lights=$270

⇒$20x+12.50y=270$...............(2)

Substitute the value of x in (2), we get

$20x+12.50(15-x)=270$

⇒$20x+187.50-12.50x=270$  [Distributive property]

⇒$20x-12.50x+187.50=270$      

⇒$7.50x+187.50=270$          

⇒$7.50x=270-187.50$         [Subtract 187.50 from both sides]

⇒$7.50x=82.50$      

⇒$x=11$        [Divide 7.50 on both sides]

Substitute x=11 in (1), we get

$y=15-11=4$

∴ The group rents 11 person tubes and 4 cooler tubes.

Answer 2

Let us represent number of one person tubes rented by x  and, number of cooler tubes rented by y    As per the situation, total tubes are 15, hence  x + y = 15 equation 1    Also, total expenditure on tubes is $270, therefore  20x + 12.5y = 270 equation 2    Linear equation written above, equation 1 and equation 2 represent given situation. Now, let us solve these equations to find number of tubes rented    Multiplying equation 1 by 20 and subtracting equation 2 from it, we get    20x + 20y - 20x -12.5y = 300 - 270    7.5y = 30  y = 4    and from equation 1, x + 4 = 15 gives, x = 11    Therefore, number of person tubes = 11, number of cooler tubes = 4