Question

Complete the steps for writing and solving a linear equation to model a real-world situation.



image.png Kayla sold several $5 bracelets and one $12 necklace. She earned $42.

How many bracelets did she sell?





Steps Work shown
1)
What information do we NOT know but is needed?

image.png The number of
Question Blank 1 of 4
choose your answer...
she sold.
2)

Represent what we don't know using the variable x.

This is called
"defining the variable"


image.png Let x represent the number of bracelets sold.
3)

Write an expression with x


image.png

Money made from items sold:

5 bracelets = $5 times x
1 necklace = $12

Total money made =
Question Blank 2 of 4
choose your answer...



4)


Solve for x


image.png x =
Question Blank 3 of 4
choose your answer...


This means Kayla sold
Question Blank 4 of 4
choose your answer...
.
5)


Check your answer.



image.png Does $5 times 6 combined with the $12 she made on the necklace equal to a total of $42?

Answer 1

Let's complete the steps for writing and solving a linear equation based on the given real-world situation involving Kayla's sales.

### Steps to Model the Situation

1) **What information do we NOT know but is needed?**

The number of **bracelets** she sold.

2) **Represent what we don't know using the variable x.**

This is called "defining the variable."

Let x represent the **number of bracelets sold**.

3) **Write an expression with x**

Money made from items sold:

- 5 bracelets = $5 times x → \(5x\)
- 1 necklace = $12

Total money made = \(5x + 12\)

4) **Solve for x**

Set up the equation based on the total earnings:
\[
5x + 12 = 42
\]

Now, solve for \(x\):
\[
5x + 12 - 12 = 42 - 12
\]
\[
5x = 30
\]
\[
x = \frac{30}{5}
\]
\[
x = 6
\]

This means Kayla sold **6 bracelets**.

5) **Check your answer.**

Does \(5 \times 6 + 12 = 42\)?

- Calculate:\(5 \times 6 = 30\)
- Adding the necklace amount: \(30 + 12 = 42\)

Yes, \(42\) is equal to \(42\), so the solution is correct.

### Summary of Answers for the Blanks:
- Question Blank 1 of 4: **bracelets**
- Question Blank 2 of 4: **5x + 12**
- Question Blank 3 of 4: **6**
- Question Blank 4 of 4: **6 bracelets**.