SOLUTION: Hi 2 similar containers P and Q were filled with rice and beans. The ratio of rice to beans in P and Q were 1:5 & 5:3 respective ly. Jug R contained 620g of beans when all the b

Question 1122626: Hi
2 similar containers P and Q were filled with rice and beans. The ratio of rice to beans in P and Q were 1:5 & 5:3 respective ly. Jug R contained 620g of beans when all the beans from P and Q were poured into R there were 1200g of beans altogether. How many grams of rice were in P.
Thanks
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Mathematically, "similar" containers means the two containers are the same shape but can be different sizes. If that were, the case, the problem could not be solved. So I assume you mean containers P and Q are identical.

The contents of container P are divided into 6 parts (1:5 rice to beans); the contents of Q are divided into 8 parts (5:3 rice to beans). The problem is most easily worked if we use a common denominator of 6 and 8 so that we can visualize the two containers divided into equal numbers of parts.

The least common denominator of 6 and 8 is 24. So consider container P to have 4 parts rice and 20 parts beans (a 1:5 ratio), and consider container Q to have 15 parts rice and 9 parts beans (a 5:3 ratio).

So together containers P and Q have 20+9=29 parts beans and 4+15=19 parts rice. When the 29 parts beans from P and Q are added to the 620g of beans already in R, there are 1200g of beans in R. So

Each "part" of each container is 20g.

The question asks for the number of grams of rice in P. P has 4 parts rice, which is 4*20 = 80g.

Answer: P had (has) 80g of rice.
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