Question
OLYMPICS In the 2010 Winter Olympic Games in Vancouver, Canada, the United States athletes won 1 more than 4 times the number of gold medals won by the French athletes. The United States won 7 more gold metals than the French. Solve the equation 7+F=4F+1
to find the number of gold medals won by the French athletes.
to find the number of gold medals won by the French athletes.
Answers
GPT-4o mini
To solve the equation \( 7 + F = 4F + 1 \), we start by isolating \( F \).
1. First, let's rearrange the equation to get all the terms involving \( F \) on one side and the constant terms on the other side. We can subtract \( F \) from both sides:
\[
7 = 4F + 1 - F
\]
which simplifies to:
\[
7 = 3F + 1
\]
2. Next, we subtract 1 from both sides:
\[
7 - 1 = 3F
\]
simplifying to:
\[
6 = 3F
\]
3. Now, we divide both sides by 3 to solve for \( F \):
\[
F = \frac{6}{3} = 2
\]
Thus, the number of gold medals won by the French athletes is \( \boxed{2} \).
1. First, let's rearrange the equation to get all the terms involving \( F \) on one side and the constant terms on the other side. We can subtract \( F \) from both sides:
\[
7 = 4F + 1 - F
\]
which simplifies to:
\[
7 = 3F + 1
\]
2. Next, we subtract 1 from both sides:
\[
7 - 1 = 3F
\]
simplifying to:
\[
6 = 3F
\]
3. Now, we divide both sides by 3 to solve for \( F \):
\[
F = \frac{6}{3} = 2
\]
Thus, the number of gold medals won by the French athletes is \( \boxed{2} \).