Let's solve this problem step by step.
We are given that Gregory's age is 5 years greater than [tex]\(\frac{1}{3}\)[/tex] of Amanda's age. Gregory is 17 years old.
First, let's denote Amanda's age by [tex]\(x\)[/tex].
According to the provided information, we can set up the following equation:
[tex]\[ \frac{1}{3} x + 5 = 17 \][/tex]
This equation states that one-third of Amanda's age plus 5 years equals 17 years (Gregory's age).
We will solve this equation to find Amanda's age:
1. Start with the equation:
[tex]\[ \frac{1}{3} x + 5 = 17 \][/tex]
2. Subtract 5 from both sides of the equation to isolate the term with [tex]\(x\)[/tex]:
[tex]\[ \frac{1}{3} x = 12 \][/tex]
3. To solve for [tex]\(x\)[/tex], multiply both sides of the equation by 3:
[tex]\[ x = 12 \times 3 \][/tex]
4. Calculate the result:
[tex]\[ x = 36 \][/tex]
Therefore, Amanda is 36 years old.
Let's verify the given multiple choice options:
A. The equation is [tex]\(\frac{1}{3}(x+5)=17\)[/tex]. Amanda is 46 years old.
B. The equation is [tex]\(\frac{1}{3} x+5=17\)[/tex]. Amanda is 36 years old.
C. The equation is [tex]\(x+\frac{1}{3} x+5=17\)[/tex]. Amanda is 9 years old.
D. The equation is [tex]\(x+\frac{1}{3}+5=17\)[/tex]. Amanda is 12 years old.
The correct option here is:
B. The equation is [tex]\(\frac{1}{3} x+5=17\)[/tex]. Amanda is 36 years old.
