SOLUTION: a woman bought some large frames for $14 each and some small frames for $7 each at a closeout sale. if sale bought 27 frames for $245, find how many of each type she bought

Algebra ->  Linear-equations -> SOLUTION: a woman bought some large frames for $14 each and some small frames for $7 each at a closeout sale. if sale bought 27 frames for $245, find how many of each type she bought      Log On


   



Question 1041234: a woman bought some large frames for $14 each and some small frames for $7 each at a closeout sale. if sale bought 27 frames for $245, find how many of each type she bought
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of large frames she bought
Let +b+ = number of small frames she bought
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(1) +a+%2B+b+=+27+
(2) +14a+%2B+7b+=+245+
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There are 2 equations and 2 unknowns
so it's solvable
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Multiply both sides of (1) by +7+
and subtract (1) from (2)
(2) +14a+%2B+7b+=+245+
(1) +-7a+-+7b+=+-189+
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+7a+=+56+
+a+=+8+
and
(1) +a+%2B+b+=+27+
(1) +8+%2B+b+=+27+
(1) +b+=+19+
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She bought 8 large frames and 19 small frames
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check:
(2) +14a+%2B+7b+=+245+
(2) +14%2A8+%2B+7%2A19+=+245+
(2) +112+%2B+133+=+245+
(2) +245+=+245+
OK