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

Answer:

2 gallons of orange juice.

Step-by-step 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, $2x=2\times4=8$

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, $3x=3\times2=6$

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.