Water distributor should use 90 gallons of $ 14 and 70 gallons of $ 3 and 140 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
Sparkling water distributor wants to make up 300 gal of sparkling water
Therefore,
x + y + z = 300 ---------- 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 300 gal of sparkling water to sell for $7.00 per gallon
Therefore,
14x + 3y + 4.5z = 2100 ------ eqn 3
Substitute eqn 2 in eqn 3
14x + 3y + 4.5(2y) = 2100
14x + 3y + 9y = 2100
14x + 12y = 2100
Divide by 2 on both sides
7x + 6y = 1050 -------- eqn 4
Substitute eqn 2 in eqn 1
x + y + 2y = 300
x + 3y = 300
Multiply both sides by 2
2x + 6y = 600 -------- eqn 5
Subtract eqn 5 from eqn 4
7x + 6y - 2x - 6y = 1050 - 600
5x = 450
x = 90
Substitute x = 90 in eqn 5
2(90) + 6y = 600
180 + 6y = 600
6y = 420
y = 70
Substitute y = 70 in eqn 2
z = 2(70)
z = 140
Thus she should use 90 gallons of $ 14 and 70 gallons of $ 3 and 140 gallons of $ 4.50