Question

3
chasidy is changing the size of the garden shown to fit more vegetables. she plans to increase the width by 25%.
a. what will the new width be?
increase in width: 8 × \boxed{} = \boxed{} feet
new width: 8 + \boxed{} = \boxed{} feet
b. how much greater is the new area?
original area: 8 × 12 = \boxed{} ft² new area: \boxed{} × 12 = \boxed{} ft²
the new area is \boxed{} square feet greater.
c. chasidy plans to add 5 more plants. if each vegetable plant requires a minimum of 1.25 square feet, will chasidy’s plan work for the new dimensions of her garden?
area needed for new plants: \boxed{} × \boxed{} = \boxed{} ft²
will chasidy’s plan work? why or why not?

Explanation:

Part A

Step1: Convert 25% to decimal

25% is equal to $0.25$ (or $\frac{25}{100}=0.25$). So the first box is $0.25$.

Step2: Calculate increase in width

Multiply the original width (8 feet) by 0.25: $8\times0.25 = 2$ feet. So the second box is $2$.

Step3: Calculate new width

Add the increase to the original width: $8 + 2=10$ feet. So the third box is $2$ and the fourth box is $10$.

Part B

Step1: Calculate original area

Original width is 8, length is 12. Area = length × width, so $8\times12 = 96$ $ft^2$.

Step2: Identify new width

From part A, new width is 10.

Step3: Calculate new area

New area = $10\times12 = 120$ $ft^2$.

Step4: Find the difference

Subtract original area from new area: $120 - 96 = 24$ $ft^2$.

Part C

Step1: Calculate area needed for new plants

Number of new plants is 5, each needs 1.25 $ft^2$. So area needed: $5\times1.25 = 6.25$ $ft^2$.

Step2: Compare with area increase

From part B, the area increased by 24 $ft^2$. Since $6.25<24$, there is enough space.

Answer:

s:

Part A

Increase in width: $8\times\boldsymbol{0.25}=\boldsymbol{2}$ feet
New width: $8 + \boldsymbol{2}=\boldsymbol{10}$ feet

Part B

Original area: $8\times12=\boldsymbol{96}$ $ft^2$
New area: $\boldsymbol{10}\times12=\boldsymbol{120}$ $ft^2$
The new area is $\boldsymbol{24}$ square feet greater.

Part C

Area needed for new plants: $\boldsymbol{5}\times\boldsymbol{1.25}=\boldsymbol{6.25}$ $ft^2$
Will Chasidy’s plan work? Yes, because the area increased by 24 $ft^2$ and only 6.25 $ft^2$ is needed for the new plants, so there is enough extra space.