Question

Micah is deciding which rooms in his house he is going to paint.

Which situation is represented by the inequality 150 ≥ 42.21 + 21.64x?

Situation 1:
Micah spends $21.64 on paintbrushes.

Paint costs $42.21 per gallon.

He can spend no more than $150 on the paint and supplies.

Situation 2:
Micah spends $42.21 on paintbrushes.

Paint costs $21.64 per gallon.

He can spend no more than $150 on the paint and supplies.

Situation 3:
Micah spends $21.64 on paintbrushes.

Paint costs $42.21 per gallon.

He must spend at least $150 on the paint and supplies.

Situation 4:
Micah spends $42.21 on paintbrushes.

Paint costs $21.64 per gallon.

He must spend at least $150 on the paint and supplies.

Answer 1

One possible situation is:

"Micah spends $42.21 on supplies and paint costs $21.64 per gallon. How many gallons of paint can he buy and not spend more than $150 total

Explanation:

We know that Micah wants to spend no more than 150. This is why 150 is greater than or equal to the expression; he wants the money he has set aside, 150, to be more than or equal to the amount he spends.

42.21 is a set cost, since it is not multiplied by a variable.

21.64 is multiplied by x; this means that it is the cost of something he will be buying more than one of, and the cost will change with each additional item.

In a painting scenario, it is likely that the number of gallons of paint would be what we are trying to find and the supplies (brushes, pans, drop cloths, etc.) would be the fixed cost.

Answer 2

Situation 2:

• Micah spends $42.21 on paintbrushes.
• Paint costs $21.64 per gallon.
• He can spend no more than $150 on the paint and supplies.

Explanation:

You want to know a situation that matches the inequality 150 ≥ 42.21 + 21.64x.

Limit

The inequality tells you the sum on the right must be less than or equal to 150. This is the same as "no more than 150". (Eliminates situations 3 and 4.)

Supplies

In the scenarios offered, the costs are the sum of some number of gallons at a cost per gallon, and some amount spent on brushes.

The cost of supplies is a one-time cost, showing in the inequality as 42.21. (Eliminates situation 1.)

The paint cost is the product of the per-gallon cost and the number of gallons. The inequality suggests that x represents the number of gallons. Its coefficient, 21.64, is the per-gallon cost.

This interpretation matches Situation 2.

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