Question

The given graph shows the area (in ft${}^2$) and the cost (in $\$$) of housing properties. If the rates fall by $\$10/f{t}^2$, then how much more area can be purchased for $\$220,000?$ ($1$ foot $=12$ inches)

• A. $220f{t}^2$
• B. $20f{t}^2$
• C. $200f{t}^2$
• D. $2000f{t}^2$

Answer 1

The correct option is C $200f{t}^2$

The graph is a straight line passing through the origin; hence, it represents a proportional relationship.

Let us consider two points on the line,
$x_1=2000,y_1=220,000;x_2=2500,y_2=275,000$
Unit rate $=\text{Slope}=\frac{\text{Rise}}{\text{Run}}=\frac{y_2-y_1}{x_2-x_1}=\frac{275,000-220,000}{2500-2000}=\frac{55,000}{500}=\$110/f{t}^2$
Area that can be purchased for $\$220,000=\frac{220,000}{110}=2000f{t}^2$
When rates fall by $\$10/f{t}^2$,
new rate per sq ft $=110-10=\$100/f{t}^2$
Area that can be purchased for $\$220,000=\frac{220,000}{100}=2200f{t}^2$
Additional area that can be purchased $=2200-2000=200f{t}^2$