A designer enlarged both the length and the width of a rectangular carpet by 50 percent. The new carpet was too large so the designer was asked to reduce its length and its width by 20 percent. By what percent was the area of the final carpet design greater than the area of the original design?
d = original dimension
d plus 50% is 1.5 d
1.5 d minus 20% is 1.2 d
1.2^2 = 1.44
final is 44% larger than original
To solve this problem, we can follow a step-by-step approach:
Step 1: Let's assume the original length of the rectangular carpet is L and the original width is W. Therefore, the original area of the carpet is A = L * W.
Step 2: The designer enlarged both the length and the width by 50 percent. This means the new length will be L + (50/100) * L = 1.5L, and the new width will be W + (50/100) * W = 1.5W.
Step 3: The area of the enlarged carpet is 1.5L * 1.5W = 2.25LW.
Step 4: The designer was asked to reduce the length and the width of the enlarged carpet by 20 percent. This means the new length will be 1.5L - (20/100) * (1.5L) = 1.2 * 1.5L = 1.8L, and the new width will be 1.5W - (20/100) * (1.5W) = 1.2 * 1.5W = 1.8W.
Step 5: The area of the final carpet design is 1.8L * 1.8W = 3.24LW.
Step 6: To find the percent increase in area, we can calculate the difference between the areas and divide it by the original area:
Percent increase = ((3.24LW - LW) / LW) * 100%
Simplifying, we have:
Percent increase = (2.24LW / LW) * 100%
Percent increase = 224%
Therefore, the area of the final carpet design is 224% greater than the area of the original design.
(3/2 * 4/5)^2 = 36/25 = 1.44
so, 44% bigger