Applications of linear equations word problems

Question

70gallons of a fruit juice mixture that is 30%
orange juice. How many gallons of the mixture should be drained and replaced with pure orange juice to make the mixture 80% orange juice? Round your answer to one decimal place, if necessary.

Answer 1

Percent is concentration, think of it as the number of oranges per gallon.

 

So in 70 gallons at 30% orange/gallon you have;

(0.3 orange/gal)*(70 gal) = 21 orange

 

If you drain (subtract) "x" gallons of that 30% orange/gallon solution you have; 

21 orange - 0.3x

 

Then add the same "x" gallons of 100% orange/gallon

 

21 orange - 0.3x + (1.0)x

 

The solution we want this equal to is 80% orange/gallon at the same 70 gallon volume

 

(0.8 orange/gal)*(70 gal) = 56 orange

 

21 orange - 0.3x + x = 56 orange

 

solve for x  to get the gallons drained and filled.

 

Equation:

 

0.3(70-x) + (1)x = 0.8(70)

21 - 0.3x + x = 56

0.7x = 35

x = 50 gal

 

Answer 2

0.30(70) - 0.30x + 1.00x = 0.80(70)

21 + 0.70x = 56

 

Can you solve for x?