Can somebody help me w/ "7/10 of the boys in a marathon race were Chinese..."

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Gigi18

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Can somebody help me w/ "7/10 of the boys in a marathon race were Chinese..."

7/10 of the boys who participated in a marathon race were Chinese. The rest of the boys were made up Eurasians and Malays in the ratio 5:7 respecrively. There were 756 more Chinese than Malay boys. Find the total number of boys who participated in th marathon race.
 
Gigi18 said:
7/10 of the boys who participated in a marathon race were Chinese. The rest of the boys were made up Eurasians and Malays in the ratio 5:7 respecrively. There were 756 more Chinese than Malay boys. Find the total number of boys who participated in th marathon race.
Click to expand...

Sure. I'll do about half of it.

C = Number of Chinese Boys
E = Number of Eurasian Boys
M = Number of Malayan Boys

Okay, you're almost done. Start translating sentences...
 
Gigi18 said:
7/10 of the boys who participated in a marathon race were Chinese. The rest of the boys were made up Eurasians and Malays in the ratio 5:7 respecrively. There were 756 more Chinese than Malay boys. Find the total number of boys who participated in th marathon race.
Click to expand...

Since you put this under Pre-algebra, it is possible that you don't know how to use variables and write equations; if that is true, it will be very helpful if you can tell us what methods you do know. That's part of the reason we ask everyone to show whatever work they have done -- it shows us what direction you are starting, and also where you have trouble.

One approach that is taught in some schools for this sort of problem involves making rectangles representing various amounts, and seeing how they fit together. If a rectangle represents all the boys, then it can be divided into 10 parts, 7 of which are labeled Chinese, and the remaining 3 Other. Then that Other part has to be divided into 12 parts, 5 marked Eurasian and 7 marked Malay. Is that something you've seen before?

If not, show us what you have seen. Maybe you have done enough with fractions that you can do it without the picture.
 
Gigi18 said:
7/10 of the boys who participated in a marathon race were Chinese. The rest of the boys were made up Eurasians and Malays in the ratio 5:7 respecrively. There were 756 more Chinese than Malay boys. Find the total number of boys who participated in th marathon race.
Click to expand...
The fraction 7/10 says that the Chinese were, to the rest, in the ratio 7:3. Draw a bar with seven boxes, and another with three boxes.

Code: 
7:3

*---*---*---*---*---*---*---*
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
*---*---*---*---*---*---*---*
|   |   |   |
|   |   |   |
|   |   |   |
|   |   |   |
*---*---*---*
For the three boxes in the bottom bar, the Eurasians were, to the Malays, in the ratio 5:7, for a total of twelve parts. To split the lower three boxes into twelve parts, draw horizontal lines.

Code: 
5:7

*---*---*---*---*---*---*---*
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
|   |   |   |   |   |   |   |
*---*---*---*---*---*---*---*
|___|___|___|
|___|___|___|
|___|___|___|
|   |   |   |
*---*---*---*
Seven of these sub-boxes stand for the number of Malays, while all seven of the larger original boxes (in the top bar) stand for the number of Chinese. If the Chinese boxes were similarly sub-divided, there would be... how many smaller boxes in the first bar? How many more of the smaller boxes is this than the number for the Malay boys? This number of boxes contains the overage of Chinese boys, being 756. So how many boys are in each of the smaller boxes?

If you get stuck, please reply showing your work in answering the questions above. Thank you! ;)
 
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