Algebra MAth Question! HELP!?

Question

The question is:

A measuring cup contains 1/5 of a cup of orange juice. It is then filled to the 1 cup mark with a mixture that contains equal amounts of orange, grapefruit, and pineapple juices. What fraction of the final mixture is orange juice?

The answer is 7/15 or .466, but how do you get that? Could you explain it step by step?

Answer 1

Amount of orange juice is 1/5th of the total + 1/3 of the remaining amount (4/5ths) of the total, so

1/5 +  1/3(4/5) = 1/5 + 4/15 = 3/15 + 4/15

= 7/15

Answer 2

If it already has 1/5 full, then there is 4/5 left. That 4/5 is divided by 3 (because you are making it up to 1 with a juice containing three "flavours"):

4/5 / 3 = 4/5 x 1/3 = 4/15

you then turn 1/5 into 15ths which is 3/15. Add 4/15 and 3/15 and you get 7/15. Hope that helps.

Answer 3

Given:

1/5 is Orange Juice to begin with.

Problem:

That means 4/5 of the cup are unused, which is filled with equal amounts of orange, grapefruit, and pineapple juice. Which separated into three can be translated into:

4/5 divided by 3 (which means you multiply the 5 by 3)

So in the mixture, you have 4/15 of orange juice. Now you have to find a common denominator for the first 1/5 of orange juice that you had. (Muliply the whole fraction by 3)

So you have 4/15 from the mixture, and 3/15 from the initial orange juice. Just add them together to get 7/15 as a final answer.

You're so smart! A+ for you!

Answer 4

well your have 1/5 < which is a fraction.  now u fill it in into a cup with other things, so it probably becomes smaller RIGHT. Now there is orange 1/5, grapfuit 1/5. pineapple juice 1/5. so you have a problem like this 1/5 + 1/5 + 1/5 so you add them up you get  15 because any time over 1 is that number Im not sure how its 7<<<< 15. that i can not help you with. I was never the best at math. I am terribly sorry.

Answer 5

Given:

1/5 -- orange juice

4/5 -- equal amts. of orange, grapefruit and pineapple juices

> (4/5) / 3 = 4/15 -- amt of orange juice added

> (4/5) - (4/15) = (12-4)/15 = 8/15 -- amt of grapefruit and pineapple juices added

Let x = the total amount of orange juice in the final mixture

(1/5)x +  (4/15)x + 8/15 = 1

Simply add 1/5 and 4/15, which are both parts orange juice:

1/5 + 4/15 = (3+4)/15   [15 is the LCD]

.: 7/15 of the final mixture is orange juice

Answer 6

I'll try to make this simple:

If 1/5 of the cup is filled, then you have 4/5 left.  You have to divide 4/5 by 3 (the three juices).  When you divide a fraction, you inverse the second number.  So what you have is 4/5 times 1/3.  that give you 4/15 per juice.  In order to figure out the exact amount of orange juice, you need to get your 1/5 into a common denominator.  That gives you 3/15.  Add that to the 4/15 portion of orange juice and you get 7/15.  Its a little complicated to write out this way, but I hope this helps.

Answer 7

4/5 divided by 3

add 1/5

(1/5) is the amount of original OJ

it then said the remaining (4/5) was divided equal between the 3 juices. So 1/3rd of the remaining 4/5ths was OJ. Divide 4/5 by 3 and get 4/15 or .2666666. Add the initial (1/5), or .2, and you get .466, or 7/15. Hope this helps

Answer 8

well you know 1/5 is orange to begin with, so just write that down and then leave it alone. now you have 4/5 left to fill with the three other juices. do a similarity equation to find the amount of each of the three mixed juices (4/5=?/3)cross multiply to find that answer then you know that there is that much total of the mixed juice, divide that by three (which is basically the fraction you already have) and add that to the original 1/5 using you least common denominator (just however you feel comfortable adding fractions)   hope this helps