Question

a rectangle measuring 2 feet long by 5 feet wide has its length and width doubled. what is the resulting change of the area of the rectangle?
the area remains the same
the area is doubled.
the area is four times larger than originally.
the area is ten times larger than originally.

if boxes of pasta sell at $0.88 per box or 4 boxes for $3.00, how much is saved, to the nearest cent, on each box by buying the boxes 4 at a time?
12 cents
13 cents
39 cents
52 cents
63 cents

Explanation:

Step1: Calculate original rectangle area

Original length $l=2$ ft, width $w=5$ ft. Area $A_1 = l \times w = 2 \times 5 = 10$ sq ft.

Step2: Calculate new rectangle area

New length $2l=4$ ft, new width $2w=10$ ft. Area $A_2 = 4 \times 10 = 40$ sq ft.

Step3: Compare new and original area

$\frac{A_2}{A_1} = \frac{40}{10} = 4$. So area is 4x larger.

Step4: Calculate per-box bulk price

4 boxes for $\$3.00$, so per box: $\frac{3.00}{4} = 0.75$ dollars, or 75 cents.

Step5: Calculate savings per box

Single box price is 88 cents. Savings = $88 - 75 = 13$ cents.

Answer:

1. The area is four times larger than originally.
2. 13 cents