i don't know how to solve this equation

Question

the length of the computer screen is 2 more than the width, if the length is increased by one but the width stays the same, the area is increased by 10 squared inches

Answer 1

Hi Meghan, this is a problem that compares areas. 

 

Given:

 

Area = Length * Width

 

Let x represent the width of the original screen.

 

Then x + 2 represents the length of the original screen.

 

A = x * (x + 2)

 

A = x² + 2x

 

Now increase the length by 1, or x + 3 is the new length. Increasing the length by one increases the area by 10 square inches.

 

Using the area formula again:

 

A + 10 = x * (x + 3)

 

Subtract 10 from both sides:

 

A = x² + 3x - 10

 

The two areas are equal in size. Then:

 

x² + 2x = x² + 3x - 10

 

The x² terms cancel out, leaving:

 

2x = 3x - 10

 

Subtract 2x from both sides:

 

0 = x - 10

 

Add 10 to both sides and rearrange:

 

x = 10

 

The length and with of the original screen:

 

The width is 10 inches.

 

The length is 12 inches.

 

Check:

 

Area of original screen:

 

A₁ = 12 * 10 = 120 square inches.

 

Area of increased screen:

 

Length of increased screen is x + 3, or 13 inches.

 

A₂ = 13 * 10 = 130 square inches.

 

A₂ is 10 square inches larger than A₁.

 

Questions?