Question

Paulina has completed 24 of the 42 math problems she was assigned for homework. She plans to finish her homework by completing 9 math problems each hour h. Write an equation to find the number of hours it will take Paulina to complete her math homework assignment.

writing and interpreting equations

Answer 1

To find the number of hours \( h \) it will take Paulina to complete her math homework assignment, we need to first determine how many math problems she has left to complete.

1. **Total problems assigned**: 42
2. **Problems completed**: 24
3. **Problems remaining**: \( 42 - 24 = 18 \)

Next, since Paulina plans to complete 9 math problems each hour, we can write the equation that relates the number of hours \( h \) to the remaining problems:

\[
9h = 18
\]

### Explanation of the equation:
- The left side, \( 9h \), represents the total number of math problems Paulina will complete in \( h \) hours, given that she completes 9 problems each hour.
- The right side, \( 18 \), represents the number of problems she still needs to complete.

### Solving the Equation:
To find \( h \), divide both sides of the equation by 9:

\[
h = \frac{18}{9}
\]

\[
h = 2
\]

### Interpretation:
It will take Paulina 2 hours to complete the remaining 18 math problems if she continues to work at her current pace of 9 problems per hour.