Let's solve this problem step by step.
a. To write an equation based on the phrase "Four times a number, n, added to 3 is 47," we translate the words into mathematical terms.
"Four times a number, n" can be represented as "4n."
"Added to 3" means we add 3 to this expression, resulting in "4n + 3."
"Is" corresponds to the equals sign, "=".
And finally, "47" is our total.
Putting this all together into an equation, we get:
[tex]\[ 4n + 3 = 47 \][/tex]
b. Now that we have our equation, we can solve for n to find the number that it represents.
Start by subtracting 3 from both sides of the equation to isolate the term that contains n:
[tex]\[ 4n + 3 - 3 = 47 - 3 \][/tex]
This simplifies to:
[tex]\[ 4n = 44 \][/tex]
Next, we want to solve for n by getting it alone on one side of the equation. To do this, divide both sides by 4:
[tex]\[ \frac{4n}{4} = \frac{44}{4} \][/tex]
This simplifies to give us the value of n:
[tex]\[ n = 11 \][/tex]
So the number represented by n is 11.
