Question

Chris makes 7 dollars per hour plus a weekly bonus of 10 dollars a week, where x is the number of hours worked and y is the total income earned.

options:

What equation represents this scenario? _______

If Chris' paycheck this week is $94, how many hours did he work? ________

Answer 1

To create the equation that represents Chris's income scenario, we can start with the information provided:

- He earns $7 per hour, which can be expressed as \( 7x \) where \( x \) is the number of hours worked.
- He also receives a weekly bonus of $10.

The total income \( y \) can be represented by the equation:

\[
y = 7x + 10
\]

Now, to determine the number of hours \( x \) Chris worked if his paycheck this week is $94, we can set \( y = 94 \) and solve for \( x \):

\[
94 = 7x + 10
\]

First, subtract 10 from both sides:

\[
94 - 10 = 7x
\]
\[
84 = 7x
\]

Next, divide both sides by 7:

\[
x = \frac{84}{7} = 12
\]

So, Chris worked **12 hours** this week.

To summarize:
- The equation is: \( y = 7x + 10 \)
- The number of hours worked is: **12 hours**.

Answer 2

Find and correct the error.


x over 4 + 6 > 3


x + 6 > 12


x > 6

options:

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12
6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12

6 should have been added first before multiplying by 4 - the true answer should be x > 36
6 should have been added first before multiplying by 4 - the true answer should be x > 36

6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4
6 should have been subtracted first before multiplying by 4 - the true answer should be x > -3/4

With inequalities you always flip the symbol at the end - the true answer should be x < 6

Answer 3

Let's go through the solution step-by-step to identify the error.

1. Start with the original inequality:

\[
\frac{x}{4} + 6 > 3
\]

2. To isolate \( \frac{x}{4} \), subtract 6 from both sides:

\[
\frac{x}{4} > 3 - 6
\]

Simplifying the right side gives:

\[
\frac{x}{4} > -3
\]

3. Next, to solve for \( x \), multiply both sides by 4 (note that we do NOT flip the inequality sign when multiplying by a positive number):

\[
x > -3 \times 4
\]

This simplifies to:

\[
x > -12
\]

Based on these steps, the correct inequality is indeed:

\[
x > -12
\]

Now, let's look at the provided options to find the correct statement regarding the error:

- **6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12.** **(correct statement)**

- The other options provided are incorrect interpretations of the inequality manipulation.

So, the correct identification of the error is:

**6 should have been subtracted first before multiplying by 4 - the true answer should be x > -12.**