https://file.aiquickdraw.com/mathbot/file/1729552807699wa65odqo.jpg

Let's solve the problem step by step:

1. **What is the constant of proportionality for this scenario?**
   - The coffee shop can make 18 cups of coffee in one hour. This means the constant of proportionality (denoted as \( k \)) is 18, since the number of coffees made is directly proportional to the number of hours worked.

   **Answer:** \( k = 18 \)

2. **Using \( x \) for the number of hours and \( y \) as the number of coffees made, write an equation in the form of \( y = kx \).**
   - In this case, \( y \) represents the number of coffees made, \( x \) represents the number of hours, and \( k = 18 \). So the equation is:
   
   \[
   y = 18x
   \]

   **Answer:** \( y = 18x \)

3. **How many coffees can the shop make in 3 hours?**
   - Using the equation \( y = 18x \), substitute \( x = 3 \) to find how many coffees the shop can make in 3 hours:
   
   \[
   y = 18 \times 3 = 54
   \]

   **Answer:** 54 coffees

Would you like further details or have any questions?

Here are five related questions you can explore:
1. How many coffees can the shop make in 5 hours?
2. If the shop can make 90 coffees in a certain number of hours, how many hours did it work?
3. How many coffees can the shop make in half an hour?
4. If the coffee shop operates for 8 hours, how many coffees can it produce in total?
5. If the shop doubles its coffee production rate, what would the new constant of proportionality be?

**Tip:** In direct proportionality problems, the relationship between two quantities is always linear. So if one doubles, the other doubles as well!

A coffee shop can make 18 cups of coffee in one hour. What is the constant of proportionality? Write an equation using x for hours and y for coffees made, and calculate how many coffees are made in 3 hours.

Explore the concept of proportionality using a coffee shop's production rate. Learn how to calculate the constant of proportionality and derive a linear equation to determine how many coffees can be made in a given number of hours. Includes calculations for 3 hours. Suitable for Grade 6-8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation