English to Algebra Solutions?

Question

1. The length of a rectangle is 3 more than twice its width. The perimeter is 48 feet.

What is the length and width of this rectangle?

2. Fifteen more than four times a number is 6 more than five times the number.

Answer 1

p=2(L+W0
48=2(2W-3+w)
24=3W-3
24+3=3W
w=27/3=9
L=2*9-3=18-3=15
---------------------------------
15-4x=6-5x
-4x+5x=6-15
x=-9

Answer 2

1)

Represent the width of the rectangle as x.

Because the length is 3 more than twice the width, represent the length as:

2x + 3

The perimeter of a rectangle is 2 * the length + 2 * the width. Using this, make an equation:

2x + 2(2x + 3) = 48

Use the distributive property:

2x + 4x + 6 = 48

Combine like terms:

6x + 6 = 48

Subtract 6 from both sides:

6x = 42

Divide by 6 on both sides to solve for x:

x = 7

This is the width of the rectangle. Using the information given, the length is 3 more than twice the width, we can make another equation:

length = 2x + 3
length = 2(7) + 3
length = 14 + 3
length = 17

This is your answer: Width = 7, Length = 17

2)

Represent the number as x.

15 more than four times the number can be represented as:

4x + 15

Five times the number can be represented as 5x.

Because 15 more than four times a number is 6 more than five times the number, we can make an equation:

4x + 15 = 5x + 6

Subtract 6 from both sides:

4x + 9 = 5x

Subtract 4x from both sides and combine like terms:

9 = x

This is your answer.

Hope this helped!

Answer 3

Hi,
Problem #1:
The formula for the perimeter, P, is:
P = 2L +2W
48 = 2L + 2W (Eq#1) ( Substituting for P.)
Now, L = 2W +3 (Twice the width + three more.)
Plug the last equation into Eq #1 in place of L.
48 =2(2W+3) +2W
48 = 4W +6 + 2W (Distributive property.)
48 = 6W +6 (Combine like terms.)
42 = 6W (Subtract 6 from each side.)
7 = W (Divide both sides by 6.)

Now, plug the number y in place of W in Eq #1.
48 = 2L +2W
48 = 2L +2(7) (Substitute.)
48 = 2L + 14
34 = 2L (Subtract 14 from each side.)
17 = L (Divide each side by 2.)

Problem #2:
Let the number be represented by x.
4 times x +15 = 5 times x +6 (Since the left side is 6 more
than 5 times x, we need to add
6 to the right side to make the
equality true. )
4x +15 = 5x +6
15-6 = 5x -4x (Subtract 6 and 4x from both sides.)
9 = x

Hope this helps.
FE.

Answer 4

1st problem:
Let x = width

Equation:
2(2x + 3 + x) = 48
2(3x + 3) = 48
6x + 6 = 48
6x = 42
x = 7

2(7) + 3 = 17

Answer: width = 7, length = 17

Proof:
2(17 + 7) = 48
2(24) = 48
48 = 48

2nd problem:
Let x = the number

Equation:
4x + 15 = 5x + 6
15 - 6 = 5x - 4x
9 = x

Answer: x is 9.

Proof:
4(9) + 15 = 5(9) + 6
36 + 15 = 45 + 6
51 = 51