Question

The ratio of Alex’s toy cars to Jim’s toy cars is 8:3. How many toy cars do they have altogether, if Alex has 40 more cars than Jim.

Answer 1

$\bf \cfrac{\textit{Alex's cars}}{\textit{Jim's cars}}=\cfrac{8}{3}\qquad \qquad \cfrac{\stackrel{\textit{40 more than \underline{j}}}{j+40}}{j}=\cfrac{8}{3}\implies 3j+120=8j \\\\\\ 120=5j\implies \cfrac{120}{5}=j\implies 24=j \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{Jim}}{j = 24}\qquad \qquad \stackrel{\textit{Alex}}{24+40\implies 64}\qquad \qquad \stackrel{\textit{altogether}}{24+64\implies 88}$

Answer 2

The total number of cars that Alex and Jim have altogether is 84 cars.

What is a ratio?

A ratio is a quantitative relationship between two different numbers that express the number of times in which a number is divisible within the other number. Sometimes ratios can be expressed in fraction form.

From the given information:

• The ratio of Alex to Jim's toy is 8 : 3
• If Alex has more toys than Jim, i.e Jim = x and Alex = x + 40.

Then, we can express them in fraction form as:

$\mathbf{\dfrac{8}{3} = \dfrac{x +40}{x}}$

8x = 3(x +40)

8x = 3x + 120

8x = 3x = 120

5x = 120

x = 120/5

x = 24

Jim = x = 24 cars

Alex = x + 40 = 24 + 40 = 64 cars.

The total number of cars they have altogether is 24+64 = 84 cars.

Learn more about ratios here:

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