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A car rental company rents small cars at 50perdayandlargecarsat 80 per day. If a total of 13 cars were rented for $920 in one day, how many large cars were rented?
4
9
6
11
9
Assume all 13 cars are small: 13 * 50 = 650. Difference from actual revenue: 920 - 650 = 270. Divide by the price gap (80 - 50 = 30): 270 / 30 = 9 large cars.
Small cars (S) = 13 total. Rent: Small (50/day),Large(80/day). Total revenue = $920.
50S+80L=920;S+L=13
Assume all 13 cars are small: 13 * 50 = 650. Difference from actual revenue: 920 - 650 = 270. Divide by the price gap (80 - 50 = 30): 270 / 30 = 9 large cars.
Confusing the price of small cars with large cars or solving for 'S' instead of 'L', which would yield 4.
Define variables and equations
Let S be the number of small cars and L be the number of large cars. Based on the problem: S+L=13 and 50S+80L=920.
S+L=13,50S+80L=920
Substitute and solve
Express S as (13тИТL) and substitute into the price equation: 50(13тИТL)+80L=920.
650тИТ50L+80L=920
Calculate L
Simplify the equation: 30L=920тИТ650=270. Therefore, L=270/30.
L=9
B is correct because solving the system of linear equations yields 9 large cars.
This logic is identical to the 'alligation' method used in mixture and quantity problems; the price gap acts as the weight.
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