Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Mr. Sloan and Ms. Morgan are teaching their classes how to write in cursive. Mr. Sloan has already taught his class 3 letters. The students in Ms. Morgan's class, who started the unit later, currently know how to write 11 letters. Mr. Sloan plans to teach his class 4 new letters per week, and Ms. Morgan intends to cover 2 new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?


In
weeks, the students in both classes will know how to write
letters in cursive.

Answer 1

To solve the problem, we can let \( x \) represent the number of weeks that pass until both classes have learned the same number of letters.

We know the following at the start:
- Mr. Sloan has already taught his class 3 letters and plans to teach 4 new letters per week.
- Ms. Morgan has already taught her class 11 letters and plans to teach 2 new letters per week.

We can write the number of letters known by each class after \( x \) weeks:

1. For Mr. Sloan's class:
\[
\text{Letters taught by Mr. Sloan} = 3 + 4x
\]

2. For Ms. Morgan's class:
\[
\text{Letters taught by Ms. Morgan} = 11 + 2x
\]

Now, we want to find out when these two quantities are equal:
\[
3 + 4x = 11 + 2x
\]

Next, we solve for \( x \):
1. Subtract \( 2x \) from both sides:
\[
3 + 2x = 11
\]

2. Subtract 3 from both sides:
\[
2x = 8
\]

3. Divide by 2:
\[
x = 4
\]

Now we know that it will take 4 weeks for both classes to know the same number of letters.

Next, we can calculate how many letters they will know at that time by substituting \( x = 4 \) into either equation. We'll use Mr. Sloan's formula:
\[
\text{Letters taught by Mr. Sloan} = 3 + 4(4) = 3 + 16 = 19
\]

Thus, in 4 weeks, the students in both classes will know how to write **19** letters in cursive.

In summary:

In **4** weeks, the students in both classes will know how to write **19** letters in cursive.