Question

A sparkling-water distributor wants to make up 400 gal of sparkling water to sell for $8.00 per gallon. She wishes to mix mix three grades of water selling $14.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as the $3.00 water. How many gallons of each should she use?

Answer 1

The sparkling-water distributor should use 160 gallons of $ 14 and 80 gallons of $ 3 and 160 gallons of $ 4.50

Solution:

Let "x" be the gallons of $ 14

Let "y" be the gallons of $ 3

Let "z" be the gallons of $ 4.5

A sparkling-water distributor wants to make up 400 gal of sparkling water

Therefore,

x + y + z = 400 --------- eqn 1

She must use twice as much of the $4.50 water as the $3.00 water

gallons of $ 4.5 = twice of gallons of $ 3

z = 2y --------- eqn 2

A sparkling-water distributor wants to make up 400 gal of sparkling water to sell for $8.00 per gallon

Therefore, we frame a equation as:

$x \times 14 + y \times 3 + z \times 4.5 = 400 \times 8$

14x + 3y + 4.5z = 3200 ----------- eqn 3

Substitute eqn 2 in eqn 3

14x + 3y + 4.5(2y) = 3200

14x + 3y + 9y = 3200

14x + 12y = 3200

Divide both sides by 2

7x + 6y = 1600 -------- eqn 4

Substitute eqn 2 in eqn 1

x + y + 2y = 400

x + 3y = 400

x = 400 - 3y ------- eqn 5

Substitute eqn 5 in eqn 4

7(400 - 3y) + 6y = 1600

2800 - 21y + 6y = 1600

15y = 1200

Divide both sides by 15

y = 80

Substitute y = 80 in eqn 5

x = 400 - 3(80)

x = 400 - 240

x = 160

Substitute y = 80 in eqn 2

z = 2(80)

z = 160

Thus she should use 160 gallons of $ 14 and 80 gallons of $ 3 and 160 gallons of $ 4.50