Word problems not my thing.

[Chief343]

Translate to an equation and solve

I am terrible at word problems these two are giving me a hard time. Please help.
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]

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]

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





Thanx,Chief343