Question

Divide 52 into two parts such that half of one part is equal to the one 11th of the other part

Answer 1

1/2 ×x =1/11 ×y
x/2 =y/11
x=2y/11
x+y=52
2y/11 +y =52
2y +11y/11 =52
13y/11 =52
y=11×52/13
y=11×4
y=44
x=2y/11
x= 2×44/11
x=2×4
x=8
x=8,y=44 is answer

Answer 2

Express the ratio in simplest form:

Ratio of the two parts = 1/11 : 1/2

Multiply the ratio by 22:

Ratio of the two parts = 2 : 11

Define x:

Let x be the constant ratio

Ratio of the two parts = 2x : 11x

Solve x:

The sum is 52

2x + 11x = 52

13x = 52

x = 4

Find the parts:

Ratio of the two parts = 2x : 11x

2x = 2(4) = 8

11x = 11(4) = 44

Answer: The two parts are 8 and 44