Question

If $(4x+3y):(3x+5y)=6:7$,Find:
(iii) y if x=27

Answer 1

Step 1: Calculate the value x
Given,
$(4x+3y):(3x+5y)=6:7$
And $x=27$
$\therefore 7\times (4x+3y)=6\times (3x+5y)$
($\because$ Product of extremes = Product of means)
Put x=27 in equation
$\Rightarrow 7\times (4\times 27+3y)$ $=6\times (3\times 27+5y)$
$\Rightarrow 7\times (108+3y)=6\times (81+5y)$
$\Rightarrow 7\times 108+7\times \left(3y\right)=6\times 81+6\times \left(5y\right)$
Using distributive property $a\times (b+c)=(a\times b)+(a\times c)]$
$756+21y=486+3y$
$756-486=30y-21y$
(By combining like terms)
$270=9y$
$9y=270$
$\Rightarrow y=\frac{270}{9}=30$
Hence, value of y is 30.