Let x = the number of FT (free throws)
x + 23 = the number of 2 pt FG
y = the number of 3 pt FG
Then we know that (x + 23) + y + x = 50 (the total number of shots)
2x + 23 + y = 50
2x + y = 27
We also know that 2(x + 23) + 3y + x = 91 (the total number of points)
2x + 46 + 3y + x = 91
3x + 3y = 45
x + y = 15
Let's solve this for y
y = 15 - x, which we can plug into the other equation:
2x + (15 - x) = 27
x + 15 = 27
x = 12
So y = 15 - x = 15 - 12 = 3
We know 12 FT were made, and 3 three pt FT were made. The number of 2 pt FG = x + 23 = 12 + 23 = 35
Michael A.
tutor
Marie, the problem asks for the number of made shots for each type of shot (2 point field goals, 3 point field goals, and 1 point foul shots). We let x = the number of 1 point foul shots, and determined that x = 12. We said let y = the number of 3 point field goals, and found that y = 3. Finally, we stated that (x + 23) = the number of 2 point field goals, and we know that (x + 23) = 12 + 23 = 35.
We can check to see if this is correct by first adding up the number of made shots (or baskets). We have:
12 + 3 + 35 = 15 + 35 = 50, which is how many shots were made according to the problem.
Next, we can see if the point total is correct.
12(1) + 3(3) + 35(2) = 12 + 9 + 70 = 21 + 70 = 91, which is the total number of points scored according to the problem.
Is this clearer now? Is there something about how we arrived at the answer that you do not understand? Please let me know. Thank you.
Report
10/09/16
Marie R.
10/08/16