Question 1

88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether, 34 children wore swimming goggles. How many girls wore swimming goggles on that day?

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Solution:

Let g be the number of girls who did the swimming competition

Let b be the number of boys who did the swimming competition

b + g =88 ----> Equation No.1

1/3b + 3/7g =34 ---->Equation No.2 

1. Multiply Equation No.2 by 3 to get==> b + 9/7g =102

2. In order to subtract Equation No.1 from Equation No.2, multiply Equation No.1 by -1 to get 

-b -g = -88 ---> Equation No. 3

 

3. Now, we are able to cancel out the variable b from both Equation No. 2 and 3

To get 9/7g = 102 --> Equation No.4

           -g= -88  ----> Equation No.5

4. Now we are able to subtract Equation No. 5 from Equation No.4 to get 2/7g = 14

5. We can now go ahead and normally solve the equation for g.....

6. After solving the equation, it is known that the number of girls who completed the swimming competition is 49

7. To find the amount of girls who wore goggles.... find 3/7 of 49

which equals: 21 girls