Word Problem for Elementary Algebra

Question

Laurel scored 47 poings in last night's basketball game. Eight of her points were scored on free throws which count as 1 point each, and the rest were scored on 2-point shots and 3-point shots. If the number of 2-point shots that Laurel made was 2 more than twice the number of 3-point shots that she made, how many 2-point shots did she make?

Answer 1

Hey Amy,

 

47 = 8 + 3t + 2(r)    t for triple (3-pointer)   r for regular (2-pointer)

 

r = 2t + 2    Substitute

 

47 = 8 + 3t + 2 (2t + 2)

 

47 = 8 + 3t + 4t + 4

 

47 = 12 + 7t     35 = 7t   t = 5

 

So far, 8 free throws, 5 3s.  That's 23 points.

 

47 = 23 + 2(r)     24 = 2r     r = 12

 

In conclusion, Laurel made 12 regular shots, 5 3-pointers, and 8 Free Throws.

 

12x2 + 5x3 + 8 = 24 + 15 + 8 = 47 points.

 

There you have it.  Good luck to you.