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

Becca should buy 27 gallons of fruit juice and 1 gallon of soda to make 28 gallons of punch at a cost of $3.25 per gallon.

Step-by-step explanation:

To determine the number of gallons of fruit juice and soda Becca should buy, we can set up a system of equations based on the given information. Let x be the number of gallons of fruit juice and y be the number of gallons of soda. The cost per gallon of punch is $3.25, so the cost of x gallons of fruit juice and y gallons of soda would be 3.25x + 3.25y. We know that Becca wants to make 28 gallons of punch, so we have the equation x + y = 28. Finally, we know that the cost of making 28 gallons of punch is $3.25 per gallon, so we have the equation 3.25x + 4y = 91 (28 * 3.25 = 91). We now have a system of equations:

x + y = 28
3.25x + 4y = 91

We can solve this system using substitution or elimination. Let's use substitution. Solve the first equation for x in terms of y: x = 28 - y. Substitute this expression for x in the second equation: 3.25(28 - y) + 4y = 91. Simplify and solve for y: 91 - 3.25y + 4y = 91.75. Combine like terms: 0.75y = 0.75. Divide by 0.75: y = 1. Plug this value of y back into the first equation to solve for x: x + 1 = 28. Subtract 1: x = 27. So, Becca should buy 27 gallons of fruit juice and 1 gallon of soda to make 28 gallons of punch at a cost of $3.25 per gallon.

Answer 2

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.