# Word problems not my thing.

#### Chief343

##### New member
Translate to an equation and solve

Thankyou

Well here they are :? :

One: Twice the square of a number minus 3 is 47. Find the number.

Two: The product of 2 consecutive even positive integers is 120. Find the integers.

I know sounds easy but looks confusing to me. Thankyou for your time.

#### soroban

##### Elite Member
Hello, Chief343!

Designate an variable for an unknown quantity.
Then try to tranlate the English into an equation.

1) Twice the square of a number minus 3 is 47. $$\displaystyle \;$$ Find the number.
Let $$\displaystyle x$$ = the number.

$$\displaystyle \;\;\underbrace{Twice}\;\underbrace{the\;square\;of\;a\;number}\;\underbrace{minus}\;3\;\underbrace{is}\;47.$$

. . . . $$\displaystyle 2$$ . . . . . . $$\displaystyle \times$$ . . . . . . $$\displaystyle x^2$$ . . . . . . . . . . . . . $$\displaystyle \,-\;\;\;3\;=\;47$$

And there is our equation! $$\displaystyle \;2x^2\,-\,3\;=\;47$$

I assume you can finish it now . . .

2) The product of 2 consecutive even positive integers is 120. $$\displaystyle \;$$ Find the integers.
Consecutive even integers "go up by twos" (so do odd integers).

Let $$\displaystyle x$$ = first even integer.
Then $$\displaystyle x\,+\,2$$ = next even integer.

$$\displaystyle \;\;\underbrace{The\;product\;of\;two\;c.e.p.\;integers}\;\underbrace{is}\;120$$

. . . . . . . . . . . . . . . $$\displaystyle x(x\,+\,2)$$ . . . . . . . . . . . . . . $$\displaystyle =\;120$$

And we have our equation: $$\displaystyle \;x(x\,+\,2)\;=\;120$$

$$\displaystyle \;\;$$Go for it!

#### Chief343

##### New member
Tankyou for your help. It was very helpful without it i dont know what i would have done.

Thanx,Chief343