Sarah and Henry share some sweets in the ratio 5:6. Sarah eats 16 of their sweets and the ratio of sweets left becomes 1:2. How many sweets did Henry have?

48 sweets

Step-by-step explanation:

Let the total number of sweets be X

Thereforee, 5X/11 + 6X/11 = X.

When Sarah ate 16 sweets, the ratio of sweets left is 1 : 2.

[(5X/11) - 16] / [6X/11] = 1/2.

Cross multiply,

10X/11 - 32 = 6X/11

10X/11 - 6X/11 = 32

4X/11 = 32

4X = 32 × 11

4X = 352

X = 352/4

X = 88

therefore, sarah = 5X/11

= (5 × 88) ÷ 11 = 440/11 = 40

Henry = 6X/11

= (6 × 88) ÷ 11

= 48

Therefore, the original ratio was:

5 : 6 = 40 : 48

Sarah ate 16 sweets, her balance is:

40 – 16 = 24

Sarah : Henry = 24:48 = 1:2

Henry has 48 sweets.