Question

A contractor combined x tons of a gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x ?

Answer 1

Answer:

The value of x would be $\frac{3}{5}y$ or $\frac{3}{8}z$

Step-by-step explanation:

Given,

x tons of 10% gravel G mixture is mixed with y ton of 2% gravel G to obtain  5% gravel mixture,

Thus, gravel G in x ton + gravel in y ton = gravel G in the resultant mixture,          

⇒ 0.1x + 0.02y = 0.05(x+y),

0.1x - 0.05x = 0.05y - 0.02y

0.05x = 0.03y

$\implies x = \frac{0.03}{0.05}y=\frac{3}{5}y----(1)$

Now, resultant mixture is z ton,

i.e. $z=x+y$

$\implies y = z - x$

From equation (1),

$x=\frac{3}{5}(z-x) = \frac{3}{5}z-\frac{3}{5}x$

$x+\frac{3}{5}x=\frac{3}{5}z$

$\frac{8}{5}x=\frac{3}{5}z$

$x=\frac{3}{8}z$