I have an algebra word problem from school and cant firure it out, can u help me???

Question

The question is

[A recipe reqires 2.5 cups of juice concentrate for every 4 cups of water. How much Juice is required to fill a 32.5-cup punch bowl?]

I know the answer is 12.5 cups because the book gave me options. but i dont know how to show my work to get to it.

thank you for all your answers. i got what i needed : )

Answer 1

2.5 + 4 = 6.5

32.5/6.5 = 5

2.2 X 5 = 12.5

Answer 2

If you said 2.5 cups of juice is required for 4 cups of water thenit will make 6.5 of punch juice.
Thus the ratio of juice : dilute juice = 2.5 : 6.5

which also means to say that juice/dilute juce = 2.5/6.5

If the dilute juice is 32.5, then let x be the amout of juice require to fill up 32.5-cup of dilute juice
2.5/6.5 = x/32.5
x=32.5*2.5/6.5
x=12.5

Answer 3

You know what you are given: The recipe, and the fact that 32.5 cups equals volume of juice concentrate plus volume of water.

A "unit" of recipe is 6.5 cups, since this is 2.5 plus 4.

Dividing 32.5 by 6.5 will give you the number of "units" of recipe you will need to make: 32.5 / 6.5 equals = 5 "units."

Five units times X 2.5 cups of juice concentrate equals 12.5 cups.

Answer 4

6.5 cups of the mix has 2.5 cups of juice, or the juice concentration is 2.5/6.5x100% (or 38.46%)

32.5 cups bowl has 32.5 x 38.46% = 12.5 cups of juice

IMPORTANT NOTE: This is the answer if the assumption is that if u mix 1 cup of water with 1 cup of juice, you will get 2 cup of mixed liquid, and that the concentration doesn't change... ie, you can use 32 cups of water + 0.5 cup of juice to make 32.5 cup of punch....

Answer 5

You can do it by adding together 2.5 and 4, then dividing 32.5 by the number you get. Then, multiply that by 2.5 to get 12.5 cups.

Answer 6

32.5/(2.5+4) = 5

Therefore, to get 32.5 cups, you will need 5 batches of juice and water, each batch will be 2.5 cups of juice and 4 cups of water.

Total juice will be 5 * 2.5 = 12.5

Answer 7

The proportion is 2.5 : 6.5
(if you mix concentrate and water, that's 6.5 cups all together)

so let x be the amount of juice

2.5 / 6.5 = x / 32.5

double each side (just getting rid of the decimals for simplicity's sake)
5/13 = 2x / 65

you'll notice 65/13 = 5
so
2x / 5
also has to be 5

2x / 5 = 5
multiply each side by 5
2x= 25

divide each side by 2
x=12.5

Ta-dah!

Answer 8

Punch is juice and water. 2.5 cups of juice for each 4 cups of water means that out of two.5+4 = 6.5 cups of punch, 2.5 are juice. The ratio of juice to p unch, 2.5/6.5, remains a similar no remember how a lot punch there is. set up this equation: 2.5/6.5=x/32.5, the position x is the style of cups of juice. remedy to get x = 12.5 cups.

Answer 9

2.5 cups/4 cups = x/32.5 cups

I hope that this helps you!

Answer 10

I think the equation should look something like "X(A + B) = C", where "A" is the juice, "B" is the water, "C" is the bowl capacity and "X" is the answer.
But I might be overcomplicating things.