how many solutions will this equation have?

Question

the length of a rectangle is 3 meters more than the width. the peremeter of the rectangle is 26 meters. if the width is b, which equation represents this situation? how many solutions will this equation have?

Answer 1

b represents the width

b + 3 represents the length

b + b + 3 = 13         one length, one width, half the perimeter

2b + 3 = 13              combine like terms

2b = 10                    subtract 3 from both sides

b = 5                        divide both sides by 2

 

How long is the rectangle?

Answer 2

Here's what we know:

l = b +3 (length is 3 meters more than width)

p = 2l + 2b (the perimeter of a rect. is the 2 lengths and 2 widths added together)

p = 26 (perimeter is 26 meters long)

 

Now that we have some values for our equation, let's plug them in:

26 = 2(b + 3) + 2b

Distribute:

26 = 2b + 6 + 2b

Combine like terms:

26 = 4b + 6

Subtract 6 from both sides:

20 = 4b

Divide both sides by 4:

5 = b

 

Now we can solve for l:

l = 5 + 3

l = 8

 

check:

26 = 2 * 8 + 2 * 5

26 = 16 + 10

26 = 26