Question

When D’Ante looked at the car lot, he noticed that for every 2 red vehicles, there were 6 grey vehicles. If there are 144 total vehicles in the parking lot, how many of them are red? How many are grey?

Answer 1

Answers:

• 36 red cars
• 108 grey cars

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Work Shown:

The ratio 2 red : 6 grey reduces to 1 red : 3 grey when we divide both parts by 2. For every 1 red car, there are 3 grey cars. There are triple as many grey compared to red.

Let x be the number of red cars. Since there are 3 times as many grey cars, this means 3x represents the number of grey cars.

The total number of cars can be represented by the expression x+3x = 4x

Set this equal to the total number of cars (144) and solve for x

4x = 144

x = 144/4

x = 36

There are 36 red cars.

Subtract that value from 144 to find 144-36 = 108 grey cars.

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An alternative way to solve:

(2 red)/(6 grey) = (x red)/( (144-x) grey)

2/6 = x/(144-x)

2(144-x) = 6x .... cross multiply

2*144 - 2*x = 6x

288 - 2x = 6x

288 = 6x+2x

288 = 8x

8x = 288

x = 288/8

x = 36

If there are 144 vehicles in the parking lot, then 36 cars are red.

Also, 144 - x = 144 - 36 = 108 cars are grey.

Answer 2

36 red cars
108 grey cars