SOLUTION: This week a carpenter made some three-legged stools and some four-legged chairs. The total number of stools and chairs was 30, and the carpenter used 103 legs in all. How many cha

Algebra ->  Probability-and-statistics -> SOLUTION: This week a carpenter made some three-legged stools and some four-legged chairs. The total number of stools and chairs was 30, and the carpenter used 103 legs in all. How many cha      Log On


   

Question 575628: This week a carpenter made some three-legged stools and some four-legged chairs. The total number of stools and chairs was 30, and the carpenter used 103 legs in all. How many chairs did the carpenter make?
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = number of stools
Let +c+ = number of chairs
given:
(1) +s+%2B+c+=+30+
(2) +3s+%2B+4c+=+103+
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Multiply both sides of (1) by +3+,
and subtract (1) from (2)
(2) +3s+%2B+4c+=+103+
(1) +-3s+-+3c+=+-90+
+c+=+13+
and
(1) +s+%2B+c+=+30+
(1) +s+%2B+13+=+30+
(1) +s+=+30+-+13+
(1) +s+=+17+
The carpenter made 17 stools and 13 chairs
check:
(2) +3s+%2B+4c+=+103+
(2) +3%2A17+%2B+4%2A13+=+103+
(2) +51+%2B+52+=+103+
(2) +103+=+103+
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
This week a carpenter made some three-legged stools and some four-legged chairs. The total number of stools and chairs was 30, and the carpenter used 103 legs in all. How many chairs did the carpenter make?
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# of stools EQ: t + f = 30
# of legs EQ:: 3t +4f = 103
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Multiply thru stools EQ be 3 to get:
3t + 3f = 3*30
3t + 4f = 103
----
subtract and solve for "f":
f = 13 (# of four-legged stools)
---
Solve for "t":
t + f = 30
t + 13 = 30
t = 17 (# of 3-legged stools)
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Cheers,
Stan H.