Question

Hannah has to make 25 gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is $1.79 per gallon, and the cost of the fruit drink is $2.49 per gallon. Hannah’s budget requires that the punch cost $2.21 per gallon. How many gallons of soda and how many gallons of fruit drink does she need?

Answer 1

She will need 10 gallons of soda and 15 gallons of fruit drink.

Explanation:

Let the volume of soda and fruit drink be x and y.

Total volume of punch = 25 gallons

x + y = 25 gallons

x + y = 25...[1]

Cost of 1 gallon of soda = $1.79

Cost of 1 gallon fruit juice = $2.49

Hannah’s budget requires that the punch cost $2.21 per gallon.

Cost of 25 gallons of punch = $2.21×25 = $55.25

$1.79x + $2.49y = $55.25

1.79x + 2.49y = 55.25..[2]

Solving equation [1] and [2] , we get:

x = 10 gallons

y = 15 gallons

She will need 10 gallons of soda and 15 gallons of fruit drink.

Answer 2

She needs 10 gallons of soda and 15 gallons of fruit

Explanation:

- Hannah has to make 25 gallons of punch for a potluck

- The punch is made of soda and fruit drink

- The cost of the soda is $1.79 per gallon

- The cost of the fruit drink is $2.49 per gallon

- Hannah’s budget requires that the punch cost $2.21 per gallon

- Assume that Hannah will use x gallons of soda and y gallons of fruit

to make the 25 gallons of punch

∵ She has to make 25 gallons of punch

- She must to use x gallons from soda and y gallons of fruit to make it

∴ x + y = 25 ⇒ (1)

∵ The cost of the soda is $1.79 per gallon

∵ The cost of the fruit drink is $2.49 per gallon

∵ The cost of the punch cost $2.21 per gallon

∴ (1.79) x + (2.49) y = 2.21(25)

∴ 1.79 x + 2.49 y = 55.25 ⇒ (2)

* Lets solve equations (1) and (2)

- Multiply equation (1) by -1.79 to eliminate x

∵ -1.79 x - 1.79 y = -44.75 ⇒ (3)

- Add equations (2) and (3) to find y

∴ 0.7 y = 10.5

- Divided both sides by 0.7

∴ y = 15

- Substitute the value of y in equation (1)

∴ x + 15 = 25

- Subtract 15 from both sides

∴ x = 10

∵ x represents the number of gallon of soda

∵ y represents the number of gallons of fruit

∴ She needs 10 gallons of soda and 15 gallons of fruit