Question

Becca wants to mix fruit juice and soda to make a punch. She can buy fruit juice for $3 a gallon and soda for $4 a gallon. If she wants to make 28 gallons of punch at a cost of $3.25 a gallon, how many gallons of fruit juice and how many gallons of soda should she buy?

Answer 1

Answer: She should buy 21 gallons of fruit juice and 7 gallons of soda.

Step-by-step explanation:

Let x be the number of gallons of fruit juice and y be the number of gallons of soda.

Then,

$x+y=28.....(1)$

$3x+4y=3.25(28)\\\Rightarrow3x+4y=91........(2)$

Multiply 3 on the both sides of equation (1), we gte

$3x+3y=84.....(3)$

Using elimination method, subtract (3) from (2), we get

$y=7$

Substitute y=7 in (1), we get $x=21$

Hence, She should buy 21 gallons of fruit juice and 7 gallons of soda.