How many gallons of a 90% antifreeze solution must be mixed with 70 gallons of 10% antifreeze to get a mixture that is 80% antifreeze?

Let x be the amount of 90% antifreeze.

After mixing we'll have a total of 70+x gallons.

The amount of "pure" antifreeze is 0.10(70) + 0.90x

We want the concentration to be 80%

Let's clear the fractions and multiply both sides by 10.

490 gallons

Check:

(.1(70)+.9(490))/(70+490) = .8, good

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9