Question

The colours of cars at a garage are in the

ratios:
white red= 7:3
red: blue = 5:2
Sam thinks the ratio of white : blue is 7 : 2
Explain the mistake that Sam has made and
give the correct ratio.

Answer 1

Explanation:

The mistake that Sam made is that he tried to find the ratio of white to blue cars by combining the ratios of white to red cars and red to blue cars. However, this method does not work because the ratios are not independent of each other.

To find the correct ratio of white to blue cars, we need to use the fact that the ratio of red to blue cars is 5:2 and the ratio of white to red cars is 7:3. We can use these ratios to find the fraction of cars that are white and blue in the garage.

Firstly, we can find the fraction of red cars by taking the ratio of red to blue cars which is 5:2 and simplifying it to 5/7.

Now we can find the fraction of white cars by taking the ratio of white to red cars which is 7:3 and simplifying it to 7/10.

Now, to find the ratio of white to blue cars, we can subtract the fraction of red cars from the fraction of white cars.

So,

(7/10) - (5/7) = (7/10) - (5/7) * (3/3) = (7/10) - (15/21) = (721 - 1510) / (210) = (147 - 150) / 210 = -3/210

The correct ratio of white to blue cars is -3/210 which can be understood as NO white cars in the garage. Sam has made an error in his calculation.