need help with word problem solving!

Question

Terry is mixing a punch which contains 3 liters of juice for every 2 liters of soda. If he wants to make 21 liters of punch, how much juice does he need?

 

 

 

A car's radiator currently contains 2 quarts of liquid which is 25% antifreeze. How many quarts of 100% antifreeze must be added to increase the antifreeze content to 60%?

Answer 1

3 liters of juice for every 2 liters of soda means that it takes 3 liters of juice per 3+2=5 liters of punch. If for preparation of 5 liters of punch 3 liters of juice is required, to determine the amount of juice necessary to prepare 21 liters of punch you should solve the equation:

 

x/21 = 3/5

x=3*21/5=12.6 liters of juice

Answer 2

3x+2x=21

5x=21

x=4.2

4.2*3=12.6 L of juice

4.2*2=8.4 L of soda

 

25% of 2 is 0.25*2=0.5 quarts of antifreeze in the 2 quart solution now

x=# of quarts of pure antifreeze to add to get a 60% solution of antifreeze

(x+0.5) must be 60% of (2+x)

(x+0.5)/(2+x)=60%

(x+0.5)/(2+x)=60/100 (60/100=3/5)

(x+0.5)/(2+x)=3/5

cross multiply

3(2+x)=5(x+0.5)

6+3x=5x+2.5

6-2.5=5x-3x

3.5=2x

35=20x

x=35/20

x=7/4

x=1 3/4 quarts of pure antifreeze must be added

check: 0.5+(1 3/4) is 60% of (2+ 1 3/4)

2.25/3.75=225/375

225/375=9/15

9/15=3/5

3/5=60/100=60%