Question 160573
The total quantity is 10lbs. This amount never changes only the composition.
X=# lbs of 40%peanuts
10-x==# lbs of 10%peanuts

Convert % to decimal format=40%=.4, 10%=.1 25%=.25

The linear equation is as follows" .40x+.1(10-x)=10(.25)

To make it easier multiply each term by a hundred. It doesn't change the equation it just makes it easier to solve.

40x+(10)(10-x)=10(25)

Use the distributive propery

40x+100-10x=250

Subtract 10x from 40x

30x+100=250

Subtract 100 from both sides of the equation

30x=150

divide both sides by 30

x=5

5lbs of 40% peanuts are needed
10-5=5lbs of 10% peanuts are needed 

To double check your answer you plug in the values in the above equation
40x+(10)(10-x)=10(25)

.4(5)+.1(5)=10(.25)

2.+.5=2.5