Slim Johnson was usually the best free-throw shooter on his basketball tam. Early in the season, however, he had made only 9 of 20 shots. By the end of the season, he had made all the additional shots he had taken, thereby ending with a season reacord of3 : 4. How many additional shots had he taken?
(9 + x)/(20 + x) = 0.75
Solve that for x, the number of additional free throws taken.
9 + x = 15 + 0.75 x
0.25 x = 6
Take it from there.
24 additional shots
Let's break down the information provided to solve the problem step-by-step:
1. At the beginning of the season, Slim Johnson had made only 9 of 20 shots.
2. This means he made 9 out of 20 shots, and missed 20 - 9 = 11 shots.
3. By the end of the season, he had made all the additional shots he had taken, resulting in a season record of 3/4.
4. This means he made 3 out of 4 additional shots taken.
5. Let's assume he took 'x' additional shots.
6. Since he made 3 out of 4 additional shots, we can write the equation: 3/4 = x/(x + 11).
7. Cross-multiplying the equation, we get 4x = 3(x + 11).
8. Expanding the equation, we get 4x = 3x + 33.
9. Subtracting 3x from both sides of the equation, we get x = 33.
10. Therefore, Slim Johnson took 33 additional shots.
In conclusion, Slim Johnson took 33 additional shots during the season.
To solve this problem, we need to find the number of additional shots Slim Johnson had taken during the season.
We know that at the beginning of the season, Slim Johnson had made 9 out of 20 shots. This means that he missed 20 - 9 = 11 shots.
By the end of the season, he had made all the additional shots he had taken, resulting in a season record of 3:4. Since the ratio of made shots to total shots is 3:4, we can set up the equation (9 + x):(20 + x) = 3:4, where x represents the additional shots he took during the season.
To simplify the equation, we can cross-multiply: 3(20 + x) = 4(9 + x).
Expanding both sides of the equation gives us: 60 + 3x = 36 + 4x.
Bringing like terms together gives: 3x - 4x = 36 - 60.
Simplifying further we get: -x = -24.
Dividing both sides by -1 gives: x = 24.
Therefore, Slim Johnson took an additional 24 shots during the season.