Answer :
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
[tex]\begin{gathered} C+U+R=274 \\ C=U-16 \\ R=U-22 \end{gathered}[/tex]1. replace equations two and three into equation 1
[tex](U-16)+U+(U-22)=274[/tex]2. Solve for U
[tex]\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 \\ \frac{3U}{3}=\frac{312}{3} \\ U=104 \end{gathered}[/tex]3. Having the value for U, we can find the value of C using equation 2
[tex]\begin{gathered} C=U-16 \\ C=104-16 \\ C=88 \end{gathered}[/tex]From the above, the answer to the question : "How many medals did China win?", the answer is 88 medals