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2 3 4 (5) 9 1 0 \( \square \) - IT 02:13 The ice skating rink charges an hourly lee for skating and \$3 10 rent skates for the day Giliafh rented skales and skaled for 3 hours and was charged \( \$ 21 \). Which equation represents the cost \( q(x) \) / of ice skating as a function of \( x \). the number of hours of skating? \( c(x)=3 x+3 \) \( c(x)=6 x+3 \) \( c(x)=7 x+3 \) \( c(x)=8 x+3 \)

Ask by Pena Turner. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The cost function is \( c(x) = 6x + 3 \).

Solution

To determine the correct equation representing the cost \( c(x) \) of ice skating as a function of \( x \) (the number of hours of skating), let's break down the information provided: 1. **Fixed Cost for Renting Skates:** \$3 2. **Total Cost for 3 Hours of Skating:** \$21 Let's denote the hourly skating fee as \( h \). The total cost \( c(x) \) can be expressed as: \[ c(x) = h \cdot x + 3 \] Given that for \( x = 3 \) hours, the total cost is \$21: \[ 21 = h \cdot 3 + 3 \] \[ 21 - 3 = 3h \] \[ 18 = 3h \] \[ h = 6 \] So, the hourly skating fee \( h \) is \$6. **Therefore, the cost function is:** \[ c(x) = 6x + 3 \] **Answer:** \( c(x) = 6x + 3 \)

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To figure out the correct equation representing the cost of ice skating, we can analyze the problem. Giliafh paid \$21 in total for 3 hours of skating and \$3 for skate rental. This means the skating sessions cost \$21 - \$3 = \$18 for 3 hours. Therefore, the hourly rate can be calculated as \$18 / 3 hours = \$6 per hour. Putting it all together, the equation for the total cost \( c(x) \) for \( x \) hours of skating would be: \[ c(x) = 6x + 3 \]. Real-world applications of this equation can be found at countless ice skating rinks! They often operate similarly, where the overall cost includes rental fees and a charge for the time spent skating. So, the equation helps you plan your skating days without blowing your budget! Now, let’s talk about a common mistake when working with these equations: confusing the components! A lot of people tend to add the rental fee to the cost per hour correctly but may overlook operational details, like sliding your rental fee into different time buckets. Always break down costs step by step to avoid these blunders!

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