Grades 9-10 Video Solutions 2014-Levels 9&10 Video Solutions 2014 problem9

Video Transcription

Question number 9. In a certain village the ratio between adult men and adult women is 2 to 3 and the ratio between adult women and children is 8 to 1.  What is the ratio between adults and children? So let's write down the information we have available. I will call the number of men here M. M for men,  W for women. Together these will be the adults. M plus W are the adults. And then we have C for children. And then the ratio 2 to 3. 2 is to 3 as men are to  women. So as M is to W. And then we also know that 8 is to 1 as women are to children. And what we have to find is compute the ratio of adults. So that is  men plus women to children. So let's begin by solving for M in terms of W and then W in terms of C, the number of children. So we have here from our first  equation we can cross multiply and we see that 2W is equal to 3M. So that 2W over 3 is equal to M. And I will write 2W over 3 plus the number of women which  is plus W. Divide that by C. And what I have now is 5W over 3 divided by C. Now from the second equation we have a relationship between children and women cross multiplying. We see  that 8C is equal to W. And I can make another replacement. So now I have 5 thirds times  W which is equal to 8C. And then I can divide by C where the C's now will cancel. And simplifying  we have 5 times 8 divided by 3 which gives me 40 over 3. And that is the final answer as the ratio between men and women so adults and children. The answer is E.

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