Question

A chemical company makes two brands of antifreeze. The first brand is 40%pure antifreeze, and the second brand is 90%pure antifreeze. In order to obtain 180gallons of a mixture that contains 55%pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

1st brand is 126 gallons

ans 2nd brand = 54 gallons

Step-by-step explanation:

given data

first brand = 40%

second brand = 90%

mixture = 55%

mixture = 180 gallons

to find out

how many gallons of each brand

solution

we consider here 1st brand is = x and 2nd brand is y

so on mixing we get

total volume = x + y ...............1

put here value

180 = x + y .................2

and mixing equation will be

40 x + 90 y = 55 ( x+ y)

solve it we get

3 x = 7 y

x =
`(7)/(3)` y ........................3

put equation 3 in equation 2

180 =
`(7)/(3)` y + y

solve it we get

y = 54

and now put in equation 2 we get

180 = x + 54

x = 126

so

1st brand is 126 gallons

ans 2nd brand = 54 gallons