SOLUTION: Please help me solve this word problem- While playing basketball, Mr. Koster scored 32 points. Points came from a combination of free throws, 2-pointers and 3-pointers. He made 19

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Question 676981: Please help me solve this word problem- While playing basketball, Mr. Koster scored 32 points. Points came from a combination of free throws, 2-pointers and 3-pointers. He made 19 baskets in total with half as many 2-pointers as free throws. How many of each type of basket did he make?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of free throws
Let +b+ = number of 2-pointers
Let +c+ = number of 3-pointers
given:
(1) +a+%2B+b+%2B+c+=+19+
(2) +a+%2B+2b+%2B+3c+=+32+
(3) +a+=+2b+
---------------
Substitute (3) into (1)
(1) +2b+%2B+b+%2B+c+=+19+
(1) +c+=+19+-+3b+
Substitute (1) and (3) into (2)
(2) +a+%2B+2b+%2B+3c+=+32+
(2) +2b+%2B+2b+%2B+3%2A%28+19+-+3b+%29+=+32+
(2) +4b+%2B+57+-+9b+=+32+
(2) +5b+=+57+-+32+
(2) +5b+=+25+
(2) +b+=+5+
and, since
(1) +c+=+19+-+3b+
(1) +c+=+19+-+3%2A5+
(1) +c+=+4+
and
(3) +a+=+2b+
(3) +a+=+2%2A5+
(3) +a+=+10+
The number of free throws is 10
The number of 2-pointers is 5
The number of 3-pointers is 4
---------------------------
check:
(2) +a+%2B+2b+%2B+3c+=+32+
(2) +10+%2B+2%2A5+%2B+3%2A4+=+32+
(2) +10+%2B+10+%2B+12+=+32+
(2) +32+=+32+
OK