Answer :
Let's break down the problem step by step:
1. Calculate the earnings on Friday night:
Leticia charges \[tex]$8 per hour. She babysat for 4 hours on Friday night. \[ \text{Earnings on Friday} = 8 \, \text{dollars/hour} \times 4 \, \text{hours} = 32 \, \text{dollars} \] 2. Calculate the earnings on Saturday: Leticia earned a total of \$[/tex]72 from babysitting on both Friday and Saturday. To find her earnings on Saturday, subtract her Friday earnings from the total earnings.
[tex]\[ \text{Earnings on Saturday} = 72 \, \text{dollars} - 32 \, \text{dollars} = 40 \, \text{dollars} \][/tex]
3. Calculate the number of hours she worked on Saturday:
We know she earns \$8 per hour. To find the number of hours she worked on Saturday, divide her Saturday earnings by her hourly rate.
[tex]\[ \text{Hours on Saturday} = \frac{40 \, \text{dollars}}{8 \, \text{dollars/hour}} = 5 \, \text{hours} \][/tex]
4. Write the equation that models this situation:
Let [tex]\( x \)[/tex] be the number of hours Leticia babysat on Saturday. Her total earnings can be expressed as follows:
[tex]\[ 8 \, \text{dollars/hour} \times (4 \, \text{hours} + x) = 72 \, \text{dollars} \][/tex]
Simplifying this, we get the equation:
[tex]\[ 8(4 + x) = 72 \][/tex]
Thus, the correct equation is [tex]\( 8(4 + x) = 72 \)[/tex] and the number of hours Leticia babysat on Saturday is 5 hours.
So, the correct answers are:
B. Equation: [tex]\(8(4 + x)=72\)[/tex]
D. Answer: 5 hours
1. Calculate the earnings on Friday night:
Leticia charges \[tex]$8 per hour. She babysat for 4 hours on Friday night. \[ \text{Earnings on Friday} = 8 \, \text{dollars/hour} \times 4 \, \text{hours} = 32 \, \text{dollars} \] 2. Calculate the earnings on Saturday: Leticia earned a total of \$[/tex]72 from babysitting on both Friday and Saturday. To find her earnings on Saturday, subtract her Friday earnings from the total earnings.
[tex]\[ \text{Earnings on Saturday} = 72 \, \text{dollars} - 32 \, \text{dollars} = 40 \, \text{dollars} \][/tex]
3. Calculate the number of hours she worked on Saturday:
We know she earns \$8 per hour. To find the number of hours she worked on Saturday, divide her Saturday earnings by her hourly rate.
[tex]\[ \text{Hours on Saturday} = \frac{40 \, \text{dollars}}{8 \, \text{dollars/hour}} = 5 \, \text{hours} \][/tex]
4. Write the equation that models this situation:
Let [tex]\( x \)[/tex] be the number of hours Leticia babysat on Saturday. Her total earnings can be expressed as follows:
[tex]\[ 8 \, \text{dollars/hour} \times (4 \, \text{hours} + x) = 72 \, \text{dollars} \][/tex]
Simplifying this, we get the equation:
[tex]\[ 8(4 + x) = 72 \][/tex]
Thus, the correct equation is [tex]\( 8(4 + x) = 72 \)[/tex] and the number of hours Leticia babysat on Saturday is 5 hours.
So, the correct answers are:
B. Equation: [tex]\(8(4 + x)=72\)[/tex]
D. Answer: 5 hours
