## Discussion

If the ratio of two numbers is 6 and their sum is 21, what is the value of the larger number?

*This question is included in Nova Math - Diagnostic: Test / Review, question #23

(A) | 1 |

(B) | ... |

(C) | ... |

(D) | ... |

(E) | ... |

(F) | ... |

The solution is

Posted: 01/07/2012 17:34

What is a ratio?

Shelby, in short: a ratio is the proportional relation one quantity will be split in. This also implies always the minimum of at least two quantities.

Dad has 100 dollar(one quantity) and says to you and your little sister, I will give it to you both( the split in two quantities) in a ratio of 1:1. You claim to your father, that the division isn't properly done this way because as you say, 'your much older than your baby sister', so you should get a larger part. Dad agrees and adjusts the ratio so the proportional relation between the money your sister gets and you will be 2:3 (two against 3).

Now we can ask 2 questions:

How much money would you have gotten if the ratio stayed 1:1?

And how much will you get now in the ratio of 2:3?

1:1 means a total of 2(=1+1) ergo for every 2, your sister gets 1 and you get 1, in this ratio both would have been given 50 dollar.

2:3 means a total of 5(=2+3) ergo for every 5, your sister gets 2 and you get 3, in this ratio your sister gets a total of 2(100/5)=40 dollar and you get or 100-40=3(100/5)=60 dollar.

Back to the real question:

If we have two numbers(quantities) let's call them A and B and their sum 21, we can write it as A + B = 21

The ratio A against B is 6 but hang on, a ratio must be a least a fraction like (7/3) or (7:3:5) when split in more than two quantities but at least two!!!! Convert 6 into a fraction becomes (6/1) now we can continue.

6:1 means a total of 7(=6+1) ergo for every 7 A gets 6 and B gets 1, we can write it as 6A + 1B = 7

A + B = 21

6A + B = 7

6(21/7) = 18

1(21/7) = 21-18 = 3

Niels

Dad has 100 dollar(one quantity) and says to you and your little sister, I will give it to you both( the split in two quantities) in a ratio of 1:1. You claim to your father, that the division isn't properly done this way because as you say, 'your much older than your baby sister', so you should get a larger part. Dad agrees and adjusts the ratio so the proportional relation between the money your sister gets and you will be 2:3 (two against 3).

Now we can ask 2 questions:

How much money would you have gotten if the ratio stayed 1:1?

And how much will you get now in the ratio of 2:3?

1:1 means a total of 2(=1+1) ergo for every 2, your sister gets 1 and you get 1, in this ratio both would have been given 50 dollar.

2:3 means a total of 5(=2+3) ergo for every 5, your sister gets 2 and you get 3, in this ratio your sister gets a total of 2(100/5)=40 dollar and you get or 100-40=3(100/5)=60 dollar.

Back to the real question:

If we have two numbers(quantities) let's call them A and B and their sum 21, we can write it as A + B = 21

The ratio A against B is 6 but hang on, a ratio must be a least a fraction like (7/3) or (7:3:5) when split in more than two quantities but at least two!!!! Convert 6 into a fraction becomes (6/1) now we can continue.

6:1 means a total of 7(=6+1) ergo for every 7 A gets 6 and B gets 1, we can write it as 6A + 1B = 7

A + B = 21

6A + B = 7

6(21/7) = 18

1(21/7) = 21-18 = 3

Niels

Posted: 12/01/2015 22:49

Reply: good explanation

At the beginning, this problem may seem difficult, but here's a simpler and shorter way to do this. If two number have a ratio of 6:1, 7 (6+1) times the least number will equal 21, so the least number has to be 3. Now's easy. Think of this proportion:

6:1=x:3, where x=18.

6:1=x:3, where x=18.

Posted: 02/03/2014 19:04

What does 'ratio' mean?

Qifei, please follow the thread. Niels Krook answered the question very thoroughly.