Question

A chemical company makes two brands of antifreeze the first brand 65% pure antifreeze the second brand is 95% pour antifreeze in order to obtain 30 gallons of mixture that contains 75% pure antifreeze how many gallons of each brand of antifreeze must be used

Answer 1

the number of gallons for 1st brand 20 gallons

the number of gallons for 2nd brand is 10 gallons

Step-by-step explanation:

1st brand = 65% pure antifreeze

let the amount of gallons used from this antifreeze = x

in terms of percentage: 65%(x)

2nd brand = 95% pure antifreeze

let the amount of gallons used from this antifreeze = y

in terms of percentage: 95%(y)

Mixture contains 75% pure antifreeze

Amount of gallons of mixture = 30

mixture maeans amount from x plus amount from y

x + y = 30 ....(equation 1)

in terms of the percentage:

75%(x + y)

The equation:

% for 1st brand + % for 2nd brand = % for mixture

65% (x) + 95%(y) = 75%(x + y)

0.65(x) + 0.95(y) = 0.75(x + y)

0.65x + 0.95y = 0.75(x + y) ...(equation 2)

from equation 1, we can make x the subject of formula:

x = 30 - y

substitute for x in (2):

0.65(30 - y) + 0.95y = 0.75(30-y + y)

19.5 - 0.65y + 0.95y = 0.75(30)

collect like terms:

19.5 + 0.3y = 22.5

0.3y = 22.5 - 19.5

0.3y = 3

divide both sides by 0.3

0.3y/0.3 = 3/0.3

y = 10

substitute for y in equation (1):

x + 10 = 30

x = 30 - 10

x = 20

Hence, the number of gallons for 1st brand 20 gallons

the number of gallons for 2nd brand is 10 gallons