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:She needs 10 gallons of soda and 15 gallons of fruitStep-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