SOLUTION: right now, susan's age is 4 years more than four times Jane's age. In 20 years, jane will be half of susan's age then. How old are they now?

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Question 725879: right now, susan's age is 4 years more than four times Jane's age. In 20 years, jane will be half of susan's age then. How old are they now?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +j+ = Jane's age now
Let +s+ = Susan's age now
+j+%2B+20+ = Jane's age in 20 years
+s+%2B+20+ = Susan's age in 20 years
--------------------------------
given:
(1) +s+=+4j+%2B+4+
(2) +j+%2B+20+=+%281%2F2%29%2A%28+s+%2B+20+%29+
----------------------------
(2) +2%2A%28+j+%2B+20+%29+=+s+%2B+20+
(2) +2j+%2B+40+=+s+%2B+20+
(2) +s+=+2j+%2B+20+
Substitute (1) into (2)
(2) +4j+%2B+4+=+2j+%2B+20+
(2) +2j+=+16+
(2) +j+=+8+
and
(1) +s+=+4j+%2B+4+
(1) +s+=+4%2A8+%2B+4+
(1) +s+=+36+
Jane is 8 and Susan is 36
check:
(2) +j+%2B+20+=+%281%2F2%29%2A%28+s+%2B+20+%29+
(2) +8+%2B+20+=+%281%2F2%29%2A%28+36+%2B+20+%29+
(2) +28+=+56%2F2+
(2) +56+=+56+
OK