SOLUTION: the sum of two numbers is 90. the first number is 2/3 of the second number. what are the numbers?

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Question 532754: the sum of two numbers is 90. the first number is 2/3 of the second number. what are the numbers?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
given:
(1) +a+%2B+b+=+90+
(2) +a+=+%282%2F3%29%2Ab+
---------------
(2) +3a+=+2b+
(2) +3a+-+2b+=+0+
Multiply both sides of (1) by 2
and add the equations
(2) +3a+-+2b+=+0+
(1) +2a+%2B+2b+=+180+
+5a+=+180+
+a+=+36+
and, since
(1) +a+%2B+b+=+90+
(1) +b+=+90+-+36+
(1) +b+=+54+
The numbers are 36 and 54
check:
(2) +a+=+%282%2F3%29%2Ab+
(2) +36+=+%282%2F3%29%2A54+
(2) +108+=+2%2A54+
(2) +108+=+108+
OK