Respuesta :
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 [tex]x[/tex]
To find how many gallons of orange juice would Jan use,
[tex]2x+ 0.5x =10\\2.5x = 10[/tex]
By dividing both sides by 2.5
[tex]x = 4[/tex],
Jan use gallons of orange juice to make 10 gallons of punch, [tex]2x=2\times4=8[/tex]
Similarly, to find how many gallons of orange juice would Matt use,
[tex]3x+2x=10\\ 5x=10[/tex]
By dividing both sides by 5
[tex]x =2[/tex]
Matt use gallons of orange juice to make 10 gallons of punch, [tex]3x=3\times2=6[/tex]
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.
