187k views
3 votes
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?

1 Answer

5 votes

Answer: 48 sweets

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.

User Mark Melgo
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.