Latanya had math and reading homework tonight. Latanya can solve each math problem in 1.5 minutes and she can read each page in 2 minutes. The number of math prolems Latanya solved is 4 more than the number of pages she read and it took her 48 minutes to complete all of her homework. Graphically solve a system of equations in order to determine the number of math problems Latanya solved, x, commax, and the number of pages she read, yy., On this question page, you will first plot two lines. Once you have plotted two lines, the answer area will appear with a sentence with blanks to fill in.
Click twice to plot each line. Click a line to delete it.
0
x
y
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Answer
Attempt 1 out of 2

Latanya solved 
 math problems and read 
 pages.

We can solve this problem by setting up a system of equations based on the given information.

### Step 1: Define Variables
- Let \( x \) represent the number of math problems Latanya solved.
- Let \( y \) represent the number of pages Latanya read.

### Step 2: Translate the problem into equations

- **Equation 1 (time constraint):**
  Latanya spends 1.5 minutes per math problem and 2 minutes per page of reading. The total time spent is 48 minutes. This gives us the equation:
  \[
  1.5x + 2y = 48
  \]

- **Equation 2 (relation between math problems and pages read):**
  The number of math problems she solved is 4 more than the number of pages she read:
  \[
  x = y + 4
  \]

### Step 3: Substitute and Solve

Now, we substitute \( x = y + 4 \) from the second equation into the first equation:

\[
1.5(y + 4) + 2y = 48
\]

Simplifying the equation:

\[
1.5y + 6 + 2y = 48
\]
\[
3.5y + 6 = 48
\]
\[
3.5y = 42
\]
\[
y = 12
\]

Now that we know \( y = 12 \), we can substitute it back into the second equation to find \( x \):

\[
x = y + 4 = 12 + 4 = 16
\]

### Step 4: Final Answer

Latanya solved **16 math problems** and read **12 pages**.

### Graphical Solution:
To graphically solve this, we need to plot the two equations:

1. The first equation \( 1.5x + 2y = 48 \) is a line, and we can rearrange it to slope-intercept form:
   \[
   y = -0.75x + 24
   \]
2. The second equation \( x = y + 4 \) can be rearranged to:
   \[
   y = x - 4
   \]

By plotting these two lines, the intersection point will give the solution \((x, y)\), which is \((16, 12)\).

Would you like details on how to plot these equations step-by-step, or do you have any questions?

---

Here are five related questions to consider:
1. What is the meaning of the slope in each equation?
2. How would the solution change if Latanya spent more time per math problem?
3. What if Latanya solved twice as many math problems as the number of pages she read?
4. How can you verify the solution using substitution?
5. How would the system change if the total time spent was different?

**Tip**: Always check the units (like minutes per problem or page) to make sure your equations are set up correctly.

Latanya had math and reading homework tonight. Latanya can solve each math problem in 1.5 minutes and she can read each page in 2 minutes. The number of math problems Latanya solved is 4 more than the number of pages she read and it took her 48 minutes to complete all of her homework. Graphically solve a system of equations in order to determine the number of math problems Latanya solved, x, and the number of pages she read, y.

Learn how to graphically solve a system of equations based on Latanya's math and reading homework. This example involves solving a linear system where Latanya spends 1.5 minutes on each math problem, 2 minutes per page of reading, and completes her homework in 48 minutes. Suitable for students in Grades 8-10.

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