Let be "f" the number five-point problems on the test and "t" the number of two-point problems on the test.
Based on the information given in the exercise, you can set up the following System of equations:
[tex]\begin{cases}5f+2t=100 \\ f+t=38\end{cases}[/tex]You can solve the System of equations using the Substitution method:
1. Solve for "t" from the second equation:
[tex]t=38-f[/tex]2. Substitute the equation obtained in step 1 into the first equation and solve for "f":
[tex]\begin{gathered} 5f+2t=100 \\ 5f+2(38-f)=100 \\ 5f+76-2f=100 \\ 3f=100-76 \\ f=\frac{24}{3} \\ \\ f=8 \end{gathered}[/tex]3. Substitute the value of "f" into the equation found in step 1 and evaluate, in order to find the value of "t":
[tex]\begin{gathered} t=38-f \\ t=38-8 \\ t=30 \end{gathered}[/tex]The answer is:
- There are 8 five-point problems.
- There are 30 two-point problems.