A student scored $$ x $$ points on his first test and $$ y $$ points on his second test. Since he did not do very well on the first one, he studied very hard for the second test. The increase in his score, $$ y-x $$, was 26 points. His average for the two tests, $$ \frac{x+y}{2} $$, was 68 points. What did he score on the first test? $$ x= $$

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To determine the score $$ x $$ on the first test, let's set up and solve the given equations step by step.

1. **Understanding the Problem:**
   - **First Test Score:** $$ x $$
   - **Second Test Score:** $$ y $$
   - **Increase in Score:** $$ y - x = 26 $$ points
   - **Average of Two Tests:** $$ \frac{x + y}{2} = 68 $$ points

2. **Setting Up the Equations:**
   - From the increase in score:
     $$
     y = x + 26 \quad \text{(Equation 1)}
     $$
   - From the average score:
     $$
     \frac{x + y}{2} = 68
     $$
     Multiply both sides by 2 to eliminate the denominator:
     $$
     x + y = 136 \quad \text{(Equation 2)}
     $$

3. **Substituting Equation 1 into Equation 2:**
   $$
   x + (x + 26) = 136
   $$
   Simplify:
   $$
   2x + 26 = 136
   $$
   Subtract 26 from both sides:
   $$
   2x = 110
   $$
   Divide by 2:
   $$
   x = 55
   $$

4. **Conclusion:**
   The student scored **55 points** on the first test.

**Answer:**  
$$ x = 55 $$
$$ x = 55 $$

A student scored points on his first test and points on his second test. Since he
did not do very well on the first one, he studied very hard for the second test. The
increase in his score, , was 26 points. His average for the two tests, , was 68
points. What did he score on the first test?

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A student scored points on his first test and points on his second test. Since he did not do very well on the first one, he studied very hard for the second test. The increase in his score, , was 26 points. His average for the two tests, , was 68 points. What did he score on the first test?