Question

Sarah and Henry share some sweets in the ratio 7:6. Sarah eats 20 of her sweets and the ratio of sweets left becomes 1:2. How many sweets did Henry have?

Answer 1

30

Explanation:

Let's say that the intial candies Sarah and Henry had were 7x and 6x respectively. Then, after Sarah ate some, Sarah and Henry had y and 2y candies respectively. From this, we can set up a system of equations.

(1) 7x - 20 = y (because Sarah ate 20 candies)

(2) 6x = 2y (because the amount of candies Henry had didn't change)

Now, we'll solve.

(3) 3x = y (I divided (2) by 2 on both sides)

(4) 7x - 20 = 3x (Substitute (3) into (2))

x = 5

We know that Henry had 6x candies, so he had 6 * 5 = 30 candies.