Answer :
Let be "a" the number of medals that Country A won, "b" the number of medals that Country B won, and "c" the number of medals that Country C won.
You can set up the following System of equations using the information given in the exercise:
[tex]\begin{cases}a+b+c=119 \\ b=c+7 \\ a=b+c+33\end{cases}[/tex]In order to solve the System of equations, you can follow these steps:
1. Substitute the second equation into the third equation:
[tex]\begin{gathered} a=b+c+33 \\ a=(c+7)+c+33 \\ a=2c+40 \end{gathered}[/tex]2. Substitute this new equation and the second original equation, into the first original equation:
[tex](2c+40)+(c+7)+c=119[/tex]3. Solve for "c":
[tex]\begin{gathered} 4c+47=119 \\ 4c=119-47 \\ \\ c=\frac{72}{4} \\ \\ c=18 \end{gathered}[/tex]4. Knowing the value of "c", you can substitute it into the second original equation and then evaluate, in order to find the value of "b":
[tex]\begin{gathered} b=(18)+7 \\ b=25 \end{gathered}[/tex]5. Knowing the value of "b" and "c", you can substitute them into the third original equation and then evaluate, in order to find the value of "a":
[tex]\begin{gathered} a=b+c+33 \\ a=(25)+(18)+33 \\ a=76 \end{gathered}[/tex]Therefore, the answer is:
- Country A won 76 medals.
- Country B won 25 medals.
- Country C won 18 medals.