# I badly need help with a couple of equations

#### mienusmotion

##### New member
They're all word problems though.

1.The area of a rectangular room, in squared metres is u²-u-20. Write expressions for the length and for the width in terms of u. Then, find the smallest whole-number value of u that yields positive values for the sides and the area of the room

2. Two intergers differ by 9. If the squares of the intergers are added, the result is 125. What are the intergers?

3. The area of a rectangle is 357 cm². The width of the rectangle is 4 cm less than the length. What are the dimensions of the rectangle?

4. A number is equal to 12 divided by 1 less than itself. What is the original number?

#### Denis

##### Senior Member

Your problems are fairly basic: show your work; we can't guess where you're stuck!

#### mienusmotion

##### New member
Basically, I dont know what to do to set it up or anything.
Except for #2 because I found some help for it.

#### Subhotosh Khan

##### Super Moderator
Staff member
mienusmotion said:
Basically, I dont know what to do to set it up or anything.

So why are you not opening your textbook and review the example problems? If you don't show us what YOU KNOW, we have to assume we need to teach you addition/multiplication - and we cannot do that.

Except for #2 because I found some help for it.

#### mmm4444bot

##### Super Moderator
Staff member
mienusmotion said:
... I dont know what to do to set it up or anything. Except for #2 ...

Hello Motion:

Okay, let's start with exercise (2). Please show us what you've got, so far.

In the meantime, exercise (1) requires you to factor the given polynomial.

For exercise (3), pick a symbol to represent the length. Subtracting 4 from this symbol gives you an expression for the width. Use the formula for finding a rectangular area to write an equation. Solve the equation.

For exercise (4), you also need to write an equation from the given information. Here's a sample exercise:

"Two different numbers can each be written as a fraction where the numerator is -27 and the denominator is 12 more than the number itself. What are these two numbers?"

Let the variable x = the unknown numbers.

Translate the given information into expressions, and write an equation.

$$\displaystyle x \; = \; \frac{-27}{x + 12}$$

Now it's simply a matter of using algebra methods that you've learned to solve the equation to discover that x = -3 or x = -9. Please write your answer as a complete sentence.

"The two numbers are -3 and -9."

Gobble, gobble,

~ Mark 