Question

1. the area of a rectangular pool is 10 more than three times its width. choose the correct set - up to represent an equation for the area of this garden. a. a = 10w + 3 b. a = 3w + 10 c. a = 10w - 3 d. a = 3w - 10
2. the area of a rectangular garden is 12 less than 4 times its perimeter. choose the correct set - up to represent an equation for the area of the pool. a. a = 12 - 4p b. a = 12p - 4 c. a = 4p - 12 d. a = 4 - 12p
3. the length of a rectangle is 10 inches more than twice a number. write the equation for the length of the rectangle.
4. the width is 5 inches less than a number. write the equation for the width of the rectangle.
5. the length of a rectangle is 8 inches less than three times a number. write the equation for the length of the rectangle.
6. the width is 4 inches more than half of a number. write the equation for the width of the rectangle.
7. the length of a square is 4x + 5. the width of the square is 2x + 15. if the length and width are the same, find the value of x. what is the side length of the square?

side length =
x =

Explanation:

Step1: Analyze problem 15

Let width be $w$. Area $A$ is 10 more than three - times width, so $A = 3w+10$.

Step2: Analyze problem 16

Let perimeter be $p$. Area $A$ is 12 less than 4 times perimeter, so $A = 4p - 12$.

Step3: Analyze problem 17

Let the number be $n$. Length $l$ is 10 inches more than twice the number, so $l=2n + 10$.

Step4: Analyze problem 18

Let the number be $n$. Width $w$ is 5 inches less than the number, so $w=n - 5$.

Step5: Analyze problem 19

Let the number be $n$. Length $l$ is 8 inches less than three times the number, so $l = 3n-8$.

Step6: Analyze problem 20

Let the number be $n$. Width $w$ is 4 inches more than half of the number, so $w=\frac{n}{2}+4$.

Step7: Analyze problem 21

For a square, length = width. So $4x + 5=2x+15$.
Subtract $2x$ from both sides: $4x-2x + 5=2x-2x + 15$, which simplifies to $2x+5 = 15$.
Subtract 5 from both sides: $2x+5 - 5=15 - 5$, so $2x=10$.
Divide both sides by 2: $\frac{2x}{2}=\frac{10}{2}$, then $x = 5$.
The side - length of the square is $4x + 5=4\times5+5=25$ (or $2x + 15=2\times5+15=25$).

Answer:

1. B. $A = 3w + 10$
2. C. $A = 4p - 12$
3. $l=2n + 10$
4. $w=n - 5$
5. $l = 3n-8$
6. $w=\frac{n}{2}+4$
7. $x = 5$, Side Length = 25