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प्रश्न
If `(5x + 4y)/(8x + 5y) = 2/3`, find the value of 4x + 7y : 9x + 2y.
योग
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उत्तर
`(5x + 4y)/(8x + 5y) = 2/3`
3(5x + 4y) = 2(8x + 5y)
15x + 12y = 16x + 10y
15x − 16x = 10y − 12y
−x = −2y
x = 2y
Substitute x = 2y
4x + 7y : 9x + 2y
Numerator:
4x + 7y
= 4(2y) + 7y
= 8y + 7y
= 15y
Denominator:
9x + 2y
= 9(2y) + 2y
= 18y + 2y
= 20y
Combine like terms in the numerator and denominator:
`(15y)/(12y)`
Cancel y:
`15/20`
`3/4`
The value of 4x + 7y : 9x + 2y is 3 : 4.
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