To identify which situation does NOT represent a proportional relationship, we need to understand what a proportional relationship is. A proportional relationship between two quantities means that the ratio of the two quantities is constant.
Let's analyze each option:
A) The amount an employee earns who makes $15.75 per hour in h hours.
- Earnings = $15.75 * h
- This relationship is proportional because the ratio of earnings to hours worked (Earnings/h) is constant at $15.75.
B) The cost of purchasing d dozen of eggs for $2.99 per dozen of eggs.
- Cost = $2.99 * d
- This is also proportional because the ratio of cost to dozens of eggs (Cost/d) is constant at $2.99.
C) The height in w weeks of a plant that gains 2.5 centimeters per week if its starting height is 10 centimeters.
- Height after w weeks = Starting height + Growth = 10 + (2.5 * w)
- This does not represent a proportional relationship because the starting height of 10 centimeters adds a fixed amount. The ratio is not constant across different values of w since the height starts at 10 cm instead of 0.
D) The number of ounces of fruit punch in c containers with 128 ounces of fruit juice in each of the containers.
- Total ounces = 128 * c
- This is proportional since the ratio of total ounces to number of containers (Total ounces/c) is constant at 128.
Based on this analysis, the situation that could NOT represent a proportional relationship is:
C The height in w weeks of a plant that gains 2.5 centimeters per week if its starting height is 10 centimeters.
1 answer