Anthony got a job babysitting. Each hour he works he will be paid $8.00. As a bonus, he will earn an additional $1.50 per hour for each child he watches. If his total hourly rate is $12.50, how many children does he watch?

Question

Write an equation in the form px+q=r to represent this problem.

(2 points)

Answer 1

To solve for the number of children Anthony watches, we can establish the following variables:

• Let \( x \) represent the number of children Anthony watches.
• The base pay per hour is $8.00.
• The bonus for each child is $1.50 per hour.

Thus, the total hourly rate (which is the sum of his base pay and the bonuses for the children he watches) can be expressed as:

\[ \text{Total Hourly Rate} = \text{Base Pay} + \text{Bonus} \] \[ 12.50 = 8.00 + 1.50x \]

To arrange this into the form \( px + q = r \), we can rewrite the equation as follows:

Subtract \( 8.00 \) from both sides:

\[ 12.50 - 8.00 = 1.50x \]

This simplifies to:

\[ 4.50 = 1.50x \]

Now, rewriting it in the standard form \( px + q = r \):

\[ 1.50x - 4.50 = 0 \]

This represents the relationship of Anthony's pay based on the number of children he watches, and can be restated as:

\[ 1.50x + (-4.50) = 0 \]

So, the final equation in the form of \( px + q = r \) is:

\[ 1.50x - 4.50 = 0 \]