Asparkling water distributor wants to make up 300 gal of sparkling water to sell for $7.00 per gallon. she wishes to mix three grades of water selling for $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?

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

Substitute x = 90 in eqn 5

2(90) + 6y = 600

180 + 6y = 600

6y = 420

Substitute y = 70 in eqn 2

z = 2(70)

Thus she should use 90 gallons of $ 14 and 70 gallons of $ 3 and 140 gallons of $ 4.50

3x + 4y -25 =0 represents the amount of change sianna should recieve