Question

jan makes a party punch that requires 2 gallons of orange juice for every 1/2 gallon of lemonade. Matta favorite party punch recipe calls for 3 gallons of orange juice for every 2 gallons of pineapple juice. if matt and jan make 10 gallons of punch, how many more gallons of orange juice would jan use than matt?

Answer 1

2 gallons of orange juice.

Explanation:

Given:

Jan makes a party punch that requires 2 gallons of orange juice for every 1/2 (0.5) gallon of lemonade.

Matt favorite party punch recipe calls for 3 gallons of orange juice for every 2 gallons of pineapple juice.

To find:

If Matt and Jan make 10 gallons of punch, how many more gallons of orange juice would Jan use than Matt?

Solution:

Jan makes a party punch by mixing orange juice and lemonade in = 2:0.5

Matt makes a party punch by mixing orange juice and pineapple juice in = 3:2

Let ratio be
`x`

To find how many gallons of orange juice would Jan use,

`2x+ 0.5x =10\\2.5x = 10`

By dividing both sides by 2.5

`x = 4`,

Jan use gallons of orange juice to make 10 gallons of punch,
`2x=2*4=8`

Similarly, to find how many gallons of orange juice would Matt use,

`3x+2x=10\\ 5x=10`

By dividing both sides by 5

`x =2`

Matt use gallons of orange juice to make 10 gallons of punch,
`3x=3*2=6`

Now, to find how many more gallons of orange juice would Jan use than Matt,

Jan use gallons of orange juice to make 10 gallons of punch - Matt use gallons of orange juice to make 10 gallons of punch

8 - 6 = 2 gallons.

Hence, Jan use 2 gallons more orange juice than Matt.