SOLUTION: The ratio of the number of red and blue candies in a jar is 7:8. If the percentage increase in the number of red and blue be 20% and 10% respectively , what will be the new ratio?

Question 1006872: The ratio of the number of red and blue candies in a jar is 7:8. If the percentage increase in the number of red and blue be 20% and 10% respectively , what will be the new ratio?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the ratio of red to blue is 7 to 8.

7 * 1.20 = 8.4

8 * 1.10 = 8.8

the new ratio is 8.4 to 8.8.

consider that there were 75 total to start with.
let r = number of red candles.
let b = number of blue candles.

with a 7 to 8 ratio, the number of red candles would be calculated as follows:
7/15 = r/75
solve for r to get r = 75 * 7 / 15 = 35.
that would make b = 75 - 35 = 40
r/b = 35/40 = 7/8.

now you have 35 red and 40 blue
35/40 is the same as 7/8 if you divide both numerator and denominator by 5.

red is increased by 20%.
red therefore becomes 35 * 1.2 = 42
blue is increased by 10%.
blue therefore becomes 40 * 1.1 = 44

the new ratio becomes 42/44.

if we did this correctly, then the ratio of 8.4/8.8 should be the same as the ratio of 42/44.

in fact, it is exactly the same.

if you multiply 8.4/8.8 by 5/5, you will get 42/44.

to see if the ratios are the same, you would normally cross multiply.

8.4/8.8 = 42/44 becomes 8.4 * 44 = 8.8 * 42 which becomes 369.6 = 369.6

that confirms the ratios are the same.

the new ratio is 8.4 / 8.8.

if the ratio has to be modeled by integers in the numerator and denominator, then you would look for the least common multiple where the numerator and the denominator are integers.

.4 * 5 = 2.0
.8 * 5 = 4.0

these appear to be the least common multiples where the ratio is an integer.

consider the multiples of 8.4 and 8.8
8.4 = 8.4, 16.8, 25.2, 33.6, 42
8.8 = 8.8, 17.6, 26.4, 35.2, 44

the least common multiple is 5 in order to get ratios where the numerator and the denominator are each integers.

not sure what they are looking for.

8.4/8.8 should be good enough, but if integers are required, then 42/44 would be better.

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