Respuesta :
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
[tex]x+y=15[/tex]
⇒[tex]y=15-x[/tex].........(1)
Cost of a person tube=$20
Cost of a cooler tube=$12.50
Total 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.
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: [tex]\rm x+y=15\;and\;20x+12.5y=270[/tex] .
Given :
- A group spends $270 to rent a total of 15 tubes.
- One person tube costs $20 and a cooler tube costs $12.50.
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:
[tex]x+y=15[/tex] ----- (1)
[tex]20x+12.5y=270[/tex] ---- (2)
By further simplification of equation (1):
[tex]x= 15-y[/tex]
Substitute the value of x in equation (2).
[tex]20(15-y)+12.5y = 270[/tex]
[tex]300-20y+12.5y=270[/tex]
[tex]7.5y=30[/tex]
[tex]y = 4[/tex]
Substitute the value of y in equation (1).
[tex]x =15-4=11[/tex]
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: [tex]\rm x+y=15\;and\;20x+12.5y=270[/tex] .
For more information, refer the link given below:
https://brainly.com/question/13738061
