Eric, Sheena and Yael are playing a game. Eric has half as many points as Sheena. Sheena has three fewer points than Yael. Together the three players have 68 points. How many points does Yael have? Use only one variable

To solve this problem using only one variable, let's define the variable and then create equations based on the problem statement.

Let \( y \) represent the number of points Yael has.

According to the problem:

1. Sheena has three fewer points than Yael, so the number of points Sheena has can be expressed as:
   \[
   y - 3
   \]

2. Eric has half as many points as Sheena, so the number of points Eric has can be expressed as:
   \[
   \frac{1}{2}(y - 3)
   \]

3. The total number of points for Eric, Sheena, and Yael is 68. Therefore, the equation for the total points is:
   \[
   \frac{1}{2}(y - 3) + (y - 3) + y = 68
   \]

Now, let's solve this equation step by step:

\[
\frac{1}{2}(y - 3) + (y - 3) + y = 68
\]

First, multiply everything by 2 to eliminate the fraction:

\[
(y - 3) + 2(y - 3) + 2y = 136
\]

Simplify and combine like terms:

\[
y - 3 + 2y - 6 + 2y = 136
\]

\[
5y - 9 = 136
\]

Add 9 to both sides:

\[
5y = 145
\]

Divide by 5:

\[
y = 29
\]

So, Yael has **29 points**.

Would you like more details on the solution, or do you have any further questions? Here are some related questions you might consider:

1. How many points does Sheena have?
2. How many points does Eric have?
3. What if Yael had 5 more points? How would that change the total?
4. If the total number of points was 100 instead of 68, how would that change Yael's points?
5. How would the equation change if Eric had twice as many points as Sheena?

**Tip:** When working with word problems, always start by defining the variables clearly and setting up equations based on the relationships described.

Learn how to solve a word problem involving Eric, Sheena, and Yael's points in a game. Discover the step-by-step solution using algebraic equations. Understand the relationships between their points and solve for Yael's points. Suitable for Grades 7-9.

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