Number of Three Point Baskets

Question

A basketball team scored 105 points during one game. There were as many two point basketballs as free throws (1 point each), and the number of three-point baskets was five less than the number of free throws. Find the number of three point baskets.

Answer 1

1. Final Score S = 105
2. Two point baskets T = Free throws F  {Eqn 1}
3. Three point baskets H = F - 5  {Eqn 2}
4. S = (3*H) + (2*T) + (1*F)   {The final score is equal to 3 times the number of three point baskets plus 2 times the number of two point baskets plus 1 times the number of free throws}
5. Now we can substitute
1. 105 = 3H + 2T + 1F
2. 105 = 3H + 2F + 1F   {substitute Eqn 1}
3. 105 = 3(F-5} + 2F + 1F  {substitute Eqn 2}
4. 105 =  3F -15 + 2F + 1F
5. 105 =  6F - 15
6. 120 = 6F
7. F =20
6. Now that we have found F, we can substitute into Eqn 2 to find H
1. H = F -5
2. H = 20 - 5
3. H = 15
7. So, the answer is # of 3 point baskets = 15
8. Just to complete things, the number of 2 points baskets T also equals 20 (because of Eqn 1).
9. Always doublecheck your work when you can:
1. Does 105 = 3(15) + 2(20) + 1(20) ?
2. 105 = 45 + 40 + 20   Yes it does.