SOLUTION: please help me answer this question: the difference between two numbers is 16. three times the larger number is seven times the smaller. what are the numbers?

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Question 989983: please help me answer this question:
the difference between two numbers is 16. three times the larger number is seven times the smaller. what are the numbers?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the larger number
Let +b+ = the smaller number
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given:
(1) +a+-+b+=+16+
(2) +3a+=+7b+
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You have 2 equation with 2 unknowns, so
it is solvable
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Add +b+ to both sides of (1)
(1) +a+=+b+%2B+16+
Substitute (1) into (2)
(2) +3%2A%28+b+%2B+16+%29+=+7b+
(2) +3b+%2B+48+=+7b+
Subtract +3b+ from both sides
(2) +4b+=+48+
(2) +b+=+12+
and
(1) +a+=+b+%2B+16+
(1) +a+=+12+%2B+16+
(1) +a+=+28+
The larger number is 28
The smaller number is 12
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check:
(1) +a+-+b+=+16+
(1) +28+-+12+=+16+
The difference is 16
and
(2) +3a+=+7b+
(2) +3%2A28+=+7%2A12+
(2) +84+=+84+
OK