The width of a rectangle is 6 in. less than its length. The perimeter is 68 in.
What is the width of the rectangle?
(not multiple choice) my answer is 14
5(a-4) - 8a = 55 (not multiple choice) my answer -25
2n-7/3 = 15 (not multiple choice) my answer is 6
coorect
w +(w+6) = 34
2 w + 6 = 34
2 w = 28
w = 14
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5 a - 20 - 8 a = 55
-3 a = 75
a = 25
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6 n - 7 = 45
6 n = 52
n = 26/3 as you wrote it
If you mean instead
(2n-7)/3 = 15
then
2 n - 7 = 45
2 n = 52
n = 26
To find the width of the rectangle, we need to set up an equation using the information given. Let's let the length of the rectangle be represented by "L".
According to the problem, the width is 6 inches less than the length, so we can represent the width as "L - 6".
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Since we're given that the perimeter is 68 inches, we can set up the equation:
68 = 2L + 2(L - 6)
Simplifying the equation:
68 = 2L + 2L - 12
68 = 4L - 12
Now, let's solve for L:
4L = 68 + 12
4L = 80
L = 20
So, the length of the rectangle is 20 inches.
To find the width, we subtract 6 from the length:
W = L - 6
W = 20 - 6
W = 14
Therefore, the width of the rectangle is 14 inches.
Regarding the equation 5(a-4) - 8a = 55:
To solve this equation, we can start by simplifying both sides:
5a - 20 - 8a = 55
Combine like terms:
-3a - 20 = 55
Next, let's isolate the variable "a":
-3a = 55 + 20
-3a = 75
Divide both sides by -3:
a = 75 / -3
a = -25
So, the value of "a" that satisfies the equation is -25.
For the equation 2n - 7/3 = 15:
To solve this equation, we can start by isolating the term with "n" by adding 7/3 to both sides:
2n - 7/3 + 7/3 = 15 + 7/3
Simplifying:
2n = 45/3 + 7/3
2n = 52/3
Next, divide both sides by 2 to solve for "n":
n = 52/3 ÷ 2
n = 52/3 × 1/2
n = 52/6
n = 8 2/3
So, the value of "n" that satisfies the equation is 8 2/3 or 8.67.