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 ?

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slicergiza slicergiza · Answer 1 · 2019-11-04T07:56:56+01:00

Answer:

The value of x would be [tex]\frac{3}{5}y[/tex] or [tex]\frac{3}{8}z[/tex]

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

[tex]\implies x = \frac{0.03}{0.05}y=\frac{3}{5}y----(1)[/tex]

Now, resultant mixture is z ton,

i.e. [tex]z=x+y[/tex]

[tex]\implies y = z - x[/tex]

From equation (1),

[tex]x=\frac{3}{5}(z-x) = \frac{3}{5}z-\frac{3}{5}x[/tex]

[tex]x+\frac{3}{5}x=\frac{3}{5}z[/tex]

[tex]\frac{8}{5}x=\frac{3}{5}z[/tex]

[tex]x=\frac{3}{8}z[/tex]