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S28462182
15.10.2020 •
Mathematics
A high school choir had a car wash to raise money. The number of trucks washed was 2 fewer than half the total number of cars and SUVs washed. They washed twice as many cars as trucks. They washed a total of 28 trucks and cars and SUVs. Let T = the number of trucks, C = the number of cars, and S = the number of SUVs washed. Which ordered triple, (T, C, S) represents the solution to the system below? Verify your answer fully in the box provided.
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Ответ:
Number of trucks = 28
Number of cars = 14
Number of SUVs = 46
Total number of vehicles = 88
Step-by-step explanation:
Let T = the number of trucks, C = the number of cars, and S = the number of SUVs washed.
We are told :
They washed twice as many cars as trucks.
Hence: T = 2C
They washed a total of 28 trucks and cars and SUVs
Number of trucks = 28
Number of Cars =
T= 2 C
C = T/2
C = 28/2
C = 14
The number of trucks washed was 2 fewer than half the total number of cars and SUVs washed.
T = 1/2(C + S) - 2
T = 28
C = 14
Hence:
28 = 1/2(14 + S) - 2
28 = 1/2(14) + 1/2(S) - 2
28 = 7 - 2 +S/2
28 - 7 + 2 = S/2
30 - 7 = S/2
23 = S/2
S = 23 × 2
S = 46
Hence, number of SUVs = 46
Total number of vehicles = 28 + 14 + 46
= 88
Ответ: