Question

Given that x : 3 : 9/2 = 15/4 : 4 1/2 : y, find the value of x and y.

Answer 1

x =
`(5)/(2)` , y =
`(27)/(4)`

Explanation:

Equate the first 2 parts of the ratios on both sides of the equation and solve for x.

Expressing the ratios in fractional form, then

`(x)/(3)` =
`((15)/(4) )/((9)/(2) )` =
`(15)/(4)` ×
`(2)/(9)` =
`(5)/(6)` ( cross- multiply )

6x = 15 ( divide both sides by 6 )

x =
`(15)/(6)` =
`(5)/(2)`

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Equate the last 2 parts of the ratios on both sides and solve for y

`((9)/(2) )/(y)` =
`(3)/((9)/(2) )` = 3 ×
`(2)/(9)` =
`(2)/(3)` ( cross- multiply )

2y =
`(9)/(2)` × 3 =
`(27)/(2)` ( divide both sides by 2 )

y =
`(27)/(4)`