Question

In the 2012 Summer Olympics, China, the United States and Russia won a combined total of 274 medals. China won 16 fewer medals than the United States, while Russia won 22 fewer medals than the United States. How many medals did China win?

Answer 1

The total number of medals won by these three countries is given by

C + U + R = 274,

Where:

C: medals won by China

U: medals won by the U.S.

R: medals won by Russia

We are told the following:

* China won 16 fewer medals than the United States, so:

C = U - 16

* Russia won 22 fewer medals than the United States, then:

R = U - 22

having the three equations above, we can solve for C

`\begin{gathered} C+U+R=274 \\ C=U-16 \\ R=U-22 \end{gathered}`

1. replace equations two and three into equation 1

`(U-16)+U+(U-22)=274`

2. Solve for U

`\begin{gathered} U-16+U+U-22=274 \\ U+U+U-16-22=274 \\ 3U-16-22=274 \\ 3U-38=274 \\ 3U-38+38=274+38 \\ 3U=312 \\ (3U)/(3)=(312)/(3) \\ U=104 \end{gathered}`

3. Having the value for U, we can find the value of C using equation 2

`\begin{gathered} C=U-16 \\ C=104-16 \\ C=88 \end{gathered}`

From the above, the answer to the question : "How many medals did China win?", the answer is 88 medals