Acompany 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?

The number of one person tube rented is 11 and the number of cooler tube rented is 4, and the system of linear equations are: .

Given :

Linear equation can be used to determine the number of each type of tube the group rents. Let the number of one person tube be x and the number of cooler tube be y.

So, from the given data following linear equations are formed:

   ----- (1)

   ---- (2)

By further simplification of equation (1):

Substitute the value of x in equation (2).

Substitute the value of y in equation (1).

Therefore, The number of one person tube rented is 11 and the number of cooler tube rented is 4, and the system of linear equations are: .

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- 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

⇒.........(1)

Cost of a person tube=$20

Cost of a cooler tube=$12.50

Total spending on tube lights=$270

⇒...............(2)

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

⇒  [Distributive property]

⇒      

⇒          

⇒         [Subtract 187.50 from both sides]

⇒      

⇒        [Divide 7.50 on both sides]

Substitute x=11 in (1), we get

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

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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