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.


Please ask if anything is unclear.
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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