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Question
If x : y = 7 : 12, find the value of 3x + 5y : 6x + 7y.
Sum
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Solution
x : y = 7 : 12
`x/y = 7/12`
`(3x + 5y)/(6x + 7y) = (3. x/y + 5)/(6. x/y + 7)`
`x/y = 7/12`
= `(3(7/12) + 5)/(6(7/12) + 7)`
Simplify numerator:
`3 xx 7/12 = 21/12`
`5 = 60/12`
So,
`21/12 + 60/12`
= `81/12`
Simplify denominator:
`6 xx 7/12 = 42/12`
`7 = 84/12`
So,
`42/12 + 84/12`
= `126/12`
Write as a ratio:
`(81/12)/(126/12)`
= `81/126`
= `9/14`
∴ 3x + 5y : 6x + 7y = 9 : 14
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