A team plays 40 matches in any year and wins` 40%` of the matches. Next year the team won sum consecutive matches and the percentage of its winning matches becomes `80%`. Find out how many matches did the team win consecutively.

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Calculate the number of matches won in the first year.
The team plays 40 matches and wins 40% of them.

\[ \text{Matches won in the first year} = 40 \times \frac{40}{100} = 40 \times 0.4 = 16 \]

### Step 2: Determine the total number of matches played in the second year.
Let \( x \) be the number of consecutive matches won in the second year. The total number of matches played in the second year is:

\[ \text{Total matches in the second year} = 40 + x \]

### Step 3: Calculate the total number of matches won after the second year.
The total number of matches won after the second year will be:

\[ \text{Total matches won} = 16 + x \]

### Step 4: Set up the equation for the winning percentage in the second year.
According to the problem, the winning percentage after the second year becomes 80%. Therefore, we can set up the following equation:

\[ \frac{16 + x}{40 + x} = \frac{80}{100} = 0.8 \]

### Step 5: Solve the equation.
Cross-multiply to eliminate the fraction:

\[ 16 + x = 0.8(40 + x) \]

Expanding the right side:

\[ 16 + x = 32 + 0.8x \]

Now, isolate \( x \):

\[ 16 + x - 0.8x = 32 \]

\[ 16 + 0.2x = 32 \]

Subtract 16 from both sides:

\[ 0.2x = 16 \]

Now, divide by 0.2:

\[ x = \frac{16}{0.2} = 80 \]

### Conclusion:
The team won **80 consecutive matches** in the second year.

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