##### How many gallons of a plant food that is 8% nitrogen must be combined with anoth

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How many gallons of a plant food that is 8% nitrogen must be combined with another plant food that is 20% nitrogen to make 10 gal of a plant food that is 17% nitrogen?

Sep 3rd, 2015

Hello!

Denote these quantities as x and y. Then

x+y=10 (gallons).

This combination contains

0.08*x + 0.20*y of nitrogen and it must be equal to

0.17*(x+y)=0.17*10=1.7.

We obtain a linear system with two variables and two equations, solve it:

x=10-y,

0.08*(10-y)+0.2*y=1.7, or

0.8-0.08*y+0.2*y=1.7,

0.12*y=0.9,

y=0.9/0.12=90/12=30/4=7.5.

And x=10-y=2.5 (gallons).

The answer: 2.5 and 7.5 gallons, respectively.

Sep 3rd, 2015

Two cyclists start from the same point and ride in opposite directions. One cyclist rides twice as fast as the other. In 2 h, they are 84 mi apart. Find the rate of each cyclist.

Sep 3rd, 2015

(x+2x)*2=84, x=84/6=14(miles/h).

So 14 and 28.

Sep 3rd, 2015

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Sep 3rd, 2015
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Sep 3rd, 2015
Oct 18th, 2017
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