College

If four times a certain number, increased by 6, is equal to 94, what is the number?

If [tex]x[/tex] represents the number, then which of the following equations could be used to solve the problem?

A. [tex]x + 6 = 4(94)[/tex]

B. [tex]4(x + 6) = 94[/tex]

C. [tex]4x + 6 = 94[/tex]

Answer :

To solve the problem, we need to translate the words into a mathematical equation and then solve for the unknown number.

The problem states: "four times a certain number, increased by 6 is equal to 94." Let's break this down:

1. Let [tex]\( x \)[/tex] represent the certain number we are looking for.
2. "Four times a certain number" in mathematical terms means [tex]\( 4x \)[/tex].
3. "Increased by 6" means we add 6 to our expression: [tex]\( 4x + 6 \)[/tex].
4. This total is equal to 94, which gives us the equation: [tex]\( 4x + 6 = 94 \)[/tex].

Now, let's solve the equation [tex]\( 4x + 6 = 94 \)[/tex] step by step:

1. Subtract 6 from both sides to isolate the term containing [tex]\( x \)[/tex]:
[tex]\[
4x = 94 - 6
\][/tex]
[tex]\[
4x = 88
\][/tex]

2. Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{88}{4}
\][/tex]
[tex]\[
x = 22
\][/tex]

Therefore, the number we are looking for is [tex]\( 22 \)[/tex]. The correct equation from the options given is [tex]\( 4x + 6 = 94 \)[/tex].

Other Questions