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)The group rents 11 person tubes and 4 cooler tubes.2) The two system of equations arex+y=1520x+12.50y=270
Explanation:-Given: x represents the number of person tubes rented and y represents the number of cooler tubes rented such that[tex]x+y=15[/tex]⇒[tex]y=15-x[/tex].........(1)Cost of a person tube=$20Cost of a cooler tube=$12.50Total spending on tube lights=$270⇒[tex]20x+12.50y=270[/tex]...............(2)Substitute the value of x in (2), we get[tex]20x+12.50(15-x)=270[/tex]⇒[tex]20x+187.50-12.50x=270[/tex]  [Distributive property]⇒[tex]20x-12.50x+187.50=270[/tex]      ⇒[tex]7.50x+187.50=270[/tex]           ⇒[tex]7.50x=270-187.50[/tex]         [Subtract 187.50 from both sides]⇒[tex]7.50x=82.50[/tex]      ⇒[tex]x=11[/tex]        [Divide 7.50 on both sides]Substitute x=11 in (1), we get[tex]y=15-11=4[/tex]∴ The group rents 11 person tubes and 4 cooler tubes.