Question

A​ sparkling-water distributor wants to make up 300 gal of sparkling water to sell for $6.00 per gallon. She wishes to mix three grades of water selling for ​$​9.00, ​$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 distributor should use 60 gallons of $3.00 water, 120 gallons of $4.50 water, and 120 gallons of $9.00 water to make up 300 gallons of sparkling water to sell for $6.00 per gallon.

Step-by-step explanation:

To find out how many gallons of each type of water the distributor should use, let's denote the amount of the $3.00 water as x gallons. Since the distributor must use twice as much of the $4.50 water, we'll denote this amount as 2x gallons. The amount of the $9.00 water will be represented as 300 - 3x gallons, because the total amount of water must be 300 gallons.

The total cost of the mixed sparkling water is $6.00 per gallon for 300 gallons, which is $1800 in total. So, the equation to represent the total cost is:

9(300 - 3x) + 4.5(2x) + 3(x) = 1800

Solving this equation:

• 2700 - 27x + 9x + 3x = 1800
• -27x + 9x + 3x = 1800 - 2700
• -15x = -900
• x = 60

Therefore, the distributor should use 60 gallons of the $3.00 water, 120 gallons ($4.50 water is twice that of $3.00 water) and 300 - 3x = 300 - 180 = 120 gallons of the $9.00 water.