16a.) A rental truck company plans to spend $16 million on 310 new vehicles. Eac

Question

16a.) A rental truck company plans to spend $16 million on 310 new vehicles. Each commercial van will cost $45,000 each small truck 40,000, and each large truck $80,000.

Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?

Write a linear system of equations. Let x be the number of vans, y be the number of small trucks, and z be the number of large trucks.

16b.) They can buy (blank) vans, (blank) small trucks, and (blank) large trucks.

Explanation / Answer

The no of van = x

No of small trucks = y

No of large trucks = z

Total no of vehicles = 310

Or, x + y + z = 310

Or, x + 2x + z = 310

Or, z = 310 - 3x

45000x + 2x*40000 + 80000z = 16000000

Or, 45x + 80x + 80z = 16000

Or, 125x + 80(310 - 3x) = 16000

Or, 125x + 24800 - 240x = 16000

Or, 115x = 8800

Or, x = 76.5 = 76..5

Z = 310 - 3 * 76.5 = 80.5

Y = 2x = 2 * 76.5 = 153

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