Solving a percent mixture problem using a system of linear equations

Question

The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 70% pure fruit juice?

First fruit drink:

Second fruit drink:

Answer 1

Think of this as 3 containers:

The 1st container is 65% and a certain number of pints which will represent x

The 2nd container is 100% and a certain number of pints which will represent y

The 3rd container is the final product that is 70% and the total number of pints which will represent 140

So, 1st +2nd=3rd

Change the percentages into decimals in order to solve

0.65x+1.0y=0.7(140) <----Eq(1)

x+y=140 <-----Eq(2)

Solve Eq(2) in terms of x:

x+y=140

y=140-x <---- this we can plug into Eq(1)

Now solve for x after you plug in y=140-x:

0.65x+1.0(140-x)=0.7(140)

0.65+140-x=98

-0.35x=-42

x=120 pints <----this can now plug into Eq(2) to find the number of pints is the 2nd container

Plug in x=120 into Eq(2):

x+y=140

120+y=140

y=20 pints

First fruit drink requires 120 pints of 65% pure juice

Second fruit drink requires 20 pints of 100% pure juice

Answer 2

X + Y = 140

0.65 X + Y = 140*0.7 = 98

0.65X + 140-X = 98

140 - 0.35X = 98

140 - 98 = 0.35X

42 = 0.35x

4200 = 35x

x = 4200/35 = 600/5 = 120

120 of the 65%

20 of the 100%