Sarah and Henry share some sweets in the ratio 7:6 . Sarah eats 24 of her sweets and the ratio of sweets left becomes 1:2 . How many sweets did Henry have?

Answer 1

Let s = number of sweets Sarah has

Let h = number of sweets Henry has

Ratio of 7:6 indicates that S:H = 7:6, which can be written as S 7. Cross products show 6s = 7h.

---- = -----

H 6

Sarah looses 24 of her sweets to her mouth, so she has S - 24 now, H hasn't lost any.

S - 24 1

-------- = ----------

H 2

Cross products show 2(s - 24) = H x 1 = H replacing that into the first equation:

6s = 7(2s - 48)

6s = 14s - 7(48)

0 = 8s - 7(48)

7(48) = 8s

7(48)/8 = 8s/8

7(6) = s

42 = s Question asked for Henry's total sweets. 6s = 7h leads you to 6(42) = 7h

Divide each side by 7

6(6) = h

h = 36

Henry had 36 sweets and didn't eat even one of them!!