Question

How many gallons of orange juice worth $1.70 per gallon should be mixed with 100 gallons worth $2.20 per gallon to produce a mixture which will sell for $2.10 per gallon?

Answer 1

x = 20 gallon of orange juice worth $1.70 per gallon

Explanation:

Let x is the total number of gallons of orange juice required at $2.10 per gallon.

As per the given information since total of 100 gallons mix is required, therefore it is needed to add (100-x) gallons of orange juice at $2.20 per gallon.

from the information given we have following equation

x($1.70)+(100-x)($2.20) = 100($2.10)

solving for x we get required equation.

1.70x + 220 - 2.2x = 210

-0.5x = -10.

x = 20

Answer 2

25 gallons

Explanation:

Let x be the number of gallons of orange juice worth $1.70 per gallon, then x gallons are worth $1.70x.

If 100 gallons of orange juice worth $2.20 per gallon, then 100 gallons are worth
`\$2.20\cdot 100=\$220`

Total cost is

`\$1.70x+\$220`

Together we will get x + 100 gallons of a mixture. This mixture we will sell for $2.10 per gallon, so, x + 100 gallons of mixture is worth $2.10(x + 100).

Thus,

`1.70x+220=2.10(x+100)\\ \\17x+2,200=21(x+100)\ [\text{Multiplied by 10}]\\ \\17x+2,200=21x+2,100\\ \\17x-21x=2,100-2,200\\ \\-4x=-100\\ \\4x=100\\ \\x=25`