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](https://tex.z-dn.net/?f=x)
To find how many gallons of orange juice would Jan use,
![2x+ 0.5x =10\\2.5x = 10](https://tex.z-dn.net/?f=2x%2B%200.5x%20%3D10%5C%5C2.5x%20%3D%2010)
By dividing both sides by 2.5
,
Jan use gallons of orange juice to make 10 gallons of punch, ![2x=2\times4=8](https://tex.z-dn.net/?f=2x%3D2%5Ctimes4%3D8)
Similarly, to find how many gallons of orange juice would Matt use,
![3x+2x=10\\ 5x=10](https://tex.z-dn.net/?f=3x%2B2x%3D10%5C%5C%205x%3D10)
By dividing both sides by 5
![x =2](https://tex.z-dn.net/?f=x%20%3D2)
Matt use gallons of orange juice to make 10 gallons of punch, ![3x=3\times2=6](https://tex.z-dn.net/?f=3x%3D3%5Ctimes2%3D6)
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.