ratios,rates and mixture problems

[jag2000]

My son has recently began pre-algebra. I'm a little rusty here and could really use some help! The Problem reads... Determine the unit rate for the fluid ounces of punch there would be in one part of the recipe if your class uses Adam's recipe.

The recipe is 4 parts lemon lime soda and 8 parts grapefruit juice.
The recipe is to serve 160 parents and children.
The students are using glasses from the cafeteria which hold 6 fluid ounces each.

Can someone give me a clue as to where to begin here? Thank you so much in advance!

 

[Deleted member 4993]

My son has recently began pre-algebra. I'm a little rusty here and could really use some help! The Problem reads... Determine the unit rate for the fluid ounces of punch there would be in one part of the recipe if your class uses Adam's recipe.

The recipe is 4 parts lemon lime soda and 8 parts grapefruit juice.
The recipe is to serve 160 parents and children.
The students are using glasses from the cafeteria which hold 6 fluid ounces each.

Can someone give me a clue as to where to begin here? Thank you so much in advance!

the unit rate for the fluid ounces .... I don't know what does that mean!!

 

[soroban]

Hello, jag2000!

Determine the unit rate for the fluid ounces of punch there would be
in one part of the recipe if your class uses Adam's recipe.

The recipe is 4 parts lemon-lime soda and 8 parts grapefruit juice.
The recipe is to serve 160 parents and children.
The students are using glasses from the cafeteria which hold 6 fluid ounces each.

I too am baffled by that phrase.

I'll rephrase the problem . . . and you tell me if I'm correct.

160 guests will be served the punch (one glass per person).
Each glass holds 6 fluid ounces of punch.
The recipe calls for 4 parts lemon-lime soda and 8 parts grapefruit juice.'

How much lemon-lime soda and grapefruit juice is needed to serve the guests?

160 guests will get 6 ounces each.
A total of \(\displaystyle 160\times6 = 960\) ounces of punch is required.

We see that recipe says the punch is \(\displaystyle \tfrac{1}{3}\) soda and \(\displaystyle \tfrac{2}{3}\) juice.

Therefore, we need: .\(\displaystyle \begin{Bmatrix}\frac{1}{3}\times 960 \:=\:320\text{ oz. of soda} \\ \frac{2}{3}\times960 \:=\:640\text{ oz. of juice} \end{Bmatrix}\)

 

[HallsofIvy]

My son has recently began pre-algebra. I'm a little rusty here and could really use some help! The Problem reads... Determine the unit rate for the fluid ounces of punch there would be in one part of the recipe if your class uses Adam's recipe.

The recipe is 4 parts lemon lime soda and 8 parts grapefruit juice.

"4 parts lemon lime soda" and "8 parts grapefruit juice" adds up to "12 parts".
Lemon lime soda is 4/12= 1/3 of the whole thing and grapefruit juice is 8/12= 2/3 of the whole thing.
Probably what is meant by "unit rate for the fluid ounces of punch" is "1/3 oz of lemon lime soda" and "2/3 oz of grapefruit juice" per oz of punch.
(actually, it sounds awful! )

The recipe is to serve 160 parents and children.
The students are using glasses from the cafeteria which hold 6 fluid ounces each.

Can someone give me a clue as to where to begin here? Thank you so much in advance!

So each glass holds (1/3)(6)= 2 oz of lemon lime soda and (2/3)(6)= 4 oz of grapefruit juice.

Assuming each person drinks one glass you will need 160(2)= 320 oz= 10 qts= 2 1/2 gals of lemon lime soda and 160(4)= 640 oz= 20 qts= 5 gal of grape fruit juice.