Question

Which situations can be represented by the proportion startfraction 8 over one-half endfraction = startfraction 4 over one-fourth endfraction check all that apply. if 8 people can wash a car in 1/4 hour, then 4 people can wash the same car in 1/2 hour. if 8 people can eat 1/2 of a watermelon, then 4 people can eat 1/4 of the watermelon. if 1/2 pound of steak costs $8, then 1/4 pound of steak costs $4. if 1/2 a pot holds 4 fluid ounces of water, then 1/4 of the pot holds 8 fluid ounces.

Answer 1

The proportion 8/0.5 = 4/0.25 is valid because both sides simplify to 16. The first three scenarios given fit this proportion as they maintain the equivalence, but the last scenario does not since it suggests an illogical increase in water as the pot size decreases.

Step-by-step explanation:

We need to determine which situations can be represented by the proportion 8/0.5 = 4/0.25. Let's simplify the proportion:

8 divided by 0.5 equals 16

4 divided by 0.25 equals 16

Since both simplify to 16, the proportion is valid. Now, let's analyze each scenario to see if they fit with the proportion:

If 8 people can wash a car in 1/4 hour, then 4 people can wash the same car in 1/2 hour. This fits the proportion because if twice as many people are washing the car, they should take half the time, maintaining the equivalence.

If 8 people can eat 1/2 of a watermelon, then 4 people can eat 1/4 of the watermelon. This also fits the proportion since half as many people would eat half as much.

If 1/2 pound of steak costs $8, then 1/4 pound of steak costs $4. This fits as it maintains the direct proportionality between weight and cost.

If 1/2 a pot holds 4 fluid ounces of water, then 1/4 of the pot holds 8 fluid ounces. This does not fit the proportion because it suggests that as the volume of the pot decreases, the amount of water it holds increases, which is illogical.

Thus, the first three scenarios fit the proportion, but the last one does not.

Answer 2

The scenarios that align with the proportion
`\((8)/((1)/(2)) = (4)/((1)/(4))\)` are: 1. 8 people washing a car in 1/4 hour, and 4 people doing so in 1/2 hour; 2. 1/2 pound of steak costing $8 and 1/4 pound costing $4.

Step-by-step explanation:

The proportion
`\((8)/((1)/(2)) = (4)/((1)/(4))\)` shows the relationship between different scenarios based on the given ratios. To validate the situations, let's examine each option:

1. For the car washing scenario, if 8 people can complete the task in
`\((1)/(4)\)` hour, the proportion confirms that 4 people will take twice the time
`(\(1/2\)`hour) to wash the same car.

2. Regarding the steak pricing, if 1/2 pound of steak costs $8, the proportion indicates that 1/4 pound of the same steak would cost half the amount, which is $4.

The proportion
`\((8)/((1)/(2)) = (4)/((1)/(4))\)` reflects the relationship between quantities or rates. It showcases that when one side of the proportion changes by a certain factor, the other side changes in a corresponding way to maintain equality. Therefore, in these two scenarios, the relationships described by the proportion hold true, confirming that 4 people washing a car in 1/2 hour and 1/4 pound of steak costing $4 align with the given proportions and scenarios.