Air-conditioning units come in sizes of whole and half tons....

Air-conditioning units come in sizes of whole and half tons. A 1-ton airconditioning unit will cool a typical $1,100 \mathrm{sq} \mathrm{ft}$ house in the southern part of the United States. What size unit would be needed to cool a 2,973 sq ft house in the southern part of the United States? (Round up to the next higher whole or half ton.)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Proportional Reasoning

This concept involves the idea that one quantity changes in direct relation to another. In applications involving scaling—such as linking an area to a requirement like air conditioning capacity—understanding the proportional relationships allows for accurate adjustments based on changes in a measured variable.

Unit Rate Calculation

Calculating a unit rate involves determining the amount of one quantity per single unit of another quantity, which in practical terms means finding how much capacity or resource is needed per unit of area. This method is essential for scaling requirements accurately.

Rounding Up to a Specified Increment

When a calculated result does not exactly match the available standard units, rounding rules are applied. In many practical applications, such as equipment sizing, the computed value is rounded up to the nearest allowable increment to ensure adequate coverage or capacity, even if the precise computed value is lower.

Transcript

Please give Ace some feedback