SOLUTION: Mindy and Susan had some beans each.if Susan give 80 beans to mindy ,the 2 girls will have the same number of beans.if mindy gives 20 beans to Susan, Susan will have 5 times as man

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Question 1112555: Mindy and Susan had some beans each.if Susan give 80 beans to mindy ,the 2 girls will have the same number of beans.if mindy gives 20 beans to Susan, Susan will have 5 times as many beans as mindy.How many beans did mindy have? and how many beans did both girls have altogether?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of beans that Mindy has to start with
Let +b+ = number of beans that Susan has to start with
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+b+-+80+ = number Susan has after +80+ go to Mindy
+a+%2B+80+ = number Mindy has after getting +80+ from Susan
+a+%2B+80+=+b+-+80+
(1) +-a+%2B+b+=+160+
------------------------------
Mindy gives +20+ to Susan, then Mindy has
+a+-+20+
+b+%2B+20+ = number Susan then has
+b+%2B+20+=+5%2A%28+a+-+20+%29+
+b+%2B+20+=+5a+-+100+
(2) +5a+-+b+=+120+
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Add (1) and (2)
(1) +-a+%2B+b+=+160+
(2) +5a+-+b+=+120+
--------------------------
+4a+=+280+
+a+=+70+
and
(1) +-a+%2B+b+=+160+
(1) +-70+%2B+b+=+160+
(1) +b+=+230+
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Mindy has 70 beans
and
+70+%2B+230+=+300+
They have 300 beans together
---------------------------------
check:
(2) +5a+-+b+=+120+
(2) +5%2A70+-+230+=+120+
(2) +350+-+230+=+120+
(2) +120+=+120+
OK