SOLUTION: ​Joe's Tire shop sells three types of tires. High performance tires sell for ​$50/tire. Ultra performance tires sell for ​$60​/tire. Extreme performance
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Question 1094421: Joe's Tire shop sells three types of tires. High performance tires sell for $50/tire. Ultra performance tires sell for $60/tire. Extreme performance tires sell for $80/tire. Last week, the revenue generated by the sales of ultra performance tires exceeded the revenue from the sale of extreme performance tires by $1600. If the tire shop sold a total of 220 tires last week for a total revenue of $13,000, how many of each type of tire were sold? Found 2 solutions by Theo, addingup:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! h = number of high performance tires.
u = number of ultra performance tires.
e = number of extreme performance tires.
your equations are:
h + u + e = 220
50 * h + 60 * u + 80 * e = 13000
60 * u - 80 * e = 1600
first equation tells you the total number of tires sold by type.
second equation tells you the total revenue generated by type.
third equation tells you that the total revenue from ultra performance tires exceeds the total revenue from extreme performance tires by 1600.
from the third equation, solve for u to get u = (1600 + 80 * e) / 60
use that relationship in the first two equations to eliminate u as a variable in those two equations.
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h + u + e = 220 becomes h + (1600 + 80 * e) / 60) + e = 220
multiply both sides of this equation by 60 to get 60 * h + 1600 + 80 * e + 60 * e = 60 * 220
combine like terms and simplify to get 60 * h + 140 * e + 1600 = 13200
subtract 1600 from both sides to get 60 * h + 140 * e = 11600
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50 * h + 60 * u + 80 * e = 13000 becomes 50 * h + 60 * (1600 + 80 * e) / 60) + 80 * e = 13000
simplify this to get 50 * h + 1600 + 80 * e + 80 * e = 13000
combine like terms to get 50 * h + 160 * e + 1600 = 13000
subtract 1600 from both sides to get 50 * h + 160 * e = 11400
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your two equations to solve simultaneously are:
60 * h + 140 * e = 11600
50 * h + 160 * e = 11400
multiply both sides of the first equation by 5 and both sides of the second equation by 6 to get:
300 * h + 700 * e = 58000
300 * h + 960 * e = 68400
subtsract first equation from the second to get:
260 * e = 10400
divide both sides by 260 to get e = 40
you already solved for u in terms of e.
that equation was u = (1600 + 80 * e) / 60
since e = 40, that equation becomes u = (1600 + 80 * 40) / 60
solve for u to get u = 80
since h + u + e = 220, then h + 80 + 40 = 220
solve for h to get h = 100
your numbers should be:
h = 100
u = 80
e = 40
if you did this correctly then everything should check out.
h + u + e = 220 becomes 100 + 80 + 40 = 220 which becomes 220 = 220
this one checks out ok.
50 * h + 60 * u + 80 * e = 13000 becomes 50 * 100 + 60 * 80 + 80 * 40 = 13000 which becomes 13000 = 13000.
this one checks out ok.
60 * u - 80 * e = 1600 becomes 60 * 80 - 80 * 40 = 1600 which becomes 1600 = 1600
this one checks out ok.
everything checks out ok so your solution is:
number of high performance tires sold is 100.
number of ultra performance tires sold is 80.
number of extreme performance tires sold is 40.
