Two grades of gasoline are mixed to make a blend with 1.50% ofa special additive

Question

Two grades of gasoline are mixed to make a blend with 1.50% ofa special additive. Combining x litres of a grade with 1.80% of theadditive to y litres of a grade with 1.00% of the additive gives 10000 L of the blend. The equations relating x and y are ..... x + y = 10 000 0.0180x + 0.0100y = 0.0150(10 000) Find x and y (to three significant digits). Two grades of gasoline are mixed to make a blend with 1.50% ofa special additive. Combining x litres of a grade with 1.80% of theadditive to y litres of a grade with 1.00% of the additive gives 10000 L of the blend. The equations relating x and y are ..... x + y = 10 000 0.0180x + 0.0100y = 0.0150(10 000) Find x and y (to three significant digits).

Explanation / Answer

x + y = 10 000
0.0180x + 0.0100y = 0.0150(10 000)

Find x and y (to 3 significant digits).


Let us solve this by substitution. If we solve for y in thefirst equation, we obtain
y = 10000 - x

We need to substitute this value in the 2nd equation for y andsolve for our x value:
0.0180x + 0.0100(10000 - x) = 150
0.0180x + 100 - 0.0100x = 150
0.0080x = 50
x = 50/0.0080 = 6250

Now plug this value in for either equation to solve for y. Obviously, the 1st equation will be easier.
x + y = 10000
6250 + y = 10000   => y = 3750

Our solution is x = 6250, y = 3750.

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