Final answer:
Matteo's reasoning is incorrect; the ratio of points to total turns did not remain the same after he scored additional points in extra turns, which can be demonstrated by comparing the ratios using cross-multiplication.
Step-by-step explanation:
The question asks whether Matteo is correct in thinking that adding 2 to both the total number of turns and the number of points keeps the ratio of points to total turns the same. Let's examine Matteo's scores.
Initially, Matteo scores 1 point in his first 3 turns, so the ratio of points to turns is 1/3. After scoring 1 point on each of his next 2 turns, his total points become 3 and his total turns become 5. Now the ratio is 3/5.
To see if the ratios are the same, we compare them by cross-multiplication:
1/3 = 3/5 ?
5 * 1 = 3 * 3 ?
5 ≠ 9
Since 5 is not equal to 9, the ratios are not the same. Therefore, Matteo's reasoning is incorrect; the ratio of points to total turns did not remain the same after adding 2 points in 2 turns.