Please help and show work

Question

Please show your work. A customer came into an auto shop requiring a quantity of anti freeze of which 8% is glycerine. this was the percentage recommended in her owners manual. The sop owner has the following a 3 litre bottle of anti freeze is 7% glycerine a 4 litre bottle of anti freeze is 20% glycerine and a bulk supple of anti freeze is 5% glycerine. The owner not wanting to miss a sale felt that she had should create an anti freeze mixture with the required percentage by combining the contents of the entire three litre bottle with the contents of the entire four liter bottle and the adding some anti freeze from the bulk supply. How many litres of anti freeze from the bulk supply must e added to create a quantity of anti freeze of which 8% is glycerine (You may assume that the shop owner has enough of the bulk supply to create the appropriate mixture.)

Answer 1

3 liters of 7% glycerine

0.07*3=0.21 liters of glycerine

4 liters of 20% glycerine

0.2*4=0.8 liters of glycerine

total glycerine is 0.21+0.8=1.01 liters of glycerine

x=amount of 5% glycerine needed

total amount of solution is 7 liters

(5%*x+1.01)/(7+x)=8%

(0.05x+1.01)/(7+x)=8/100

cross multiply

100(0.05x+1.01)=8(7+x)

5x+101=56+8x

101-56=8x-5x

3x=45

x=45/3

x=15 liters of 5% glycerine (answer)

check: 5%*15=0.05*15=0.75 liters of glycerine

1.01+0.75=1.76 liters of glycerine

7+15=22 liters of solution

1.76/22=176/2200=44/550=4/50=8/100=8% glycerine solution