Respuesta :
Answer:
She needs 10 gallons of soda and 15 gallons of fruit
Step-by-step 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
Answer:
She will need 10 gallons of soda and 15 gallons of fruit drink.
Step-by-step 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.
