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A construction company uses regular and dually trucks (trucks that have 2 tires in the back on each side, so have 6 tires total). Altogether they have 73 trucks. They are planning to replace the tires on all their vehicles and have ordered 354 tires. If the regular trucks have 4 tires each and the dually's have 6 tires each, how many of each type of truck do they own?

Respuesta :

Answer: See explanation

Step-by-step explanation:

Let the number of regular trucks be a

Let the number of dually trucks be b.

From the question,

a + b = 73 .......... i

4a + 6b = 354 .......... ii

Multiply equation i by 4

Multiply equation ii by 1

4a + 4b = 292 ........ iii

4a + 6b = 354 ........ iv

Subtract iii from iv

2b = 62

b = 62/2

b = 31

The number of dually trucks = 31

Since a + b = 73

a + 31 = 73

a = 73 - 31

a = 42

The number of regular trucks = 42