SOLUTION: Hi anna had 3 times as many beads as zoe.they had 480 beads altogether. Mrs taylor gave an equal number of beads to each of them. Zoe then had half the number that anna had.how ma

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Question 1046396: Hi
anna had 3 times as many beads as zoe.they had 480 beads altogether. Mrs taylor gave an equal number of beads to each of them. Zoe then had half the number that anna had.how many beads did mrs taylor give them.
Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of beads that Anna
had originally
Let +b+ = number of beads that Zoe
had originally
----------------------
(1) +a+=+3b+
(2) +a+%2B+b+=+480+
----------------------
+3b+%2B+b+=+480+
+4b+=+480+
+b+=+120+
and
(1) +a+=+3b+
(1) +a+=+3%2A120+
(1) +a+=+360+
---------------------
Let +n+ = the equal number of beads
that mrs Taylor then gave them
(3) +b+%2B+n+=+%281%2F2%29%2A%28++a+%2B+n+%29+
(3) +2b+%2B+2n+=+a+%2B+n+
(3) +n+=+a+-+2b+
(3) +n+=+360+-+2%2A120+
(3) +n+=+360+-+240+
(3) +n+=+120+
------------------------
+b+%2Bn+=+120+%2B+120+=+240+
and
+a+%2B+n+=+360+%2B+120+=+480+
-----------------------------
Mrs Taylor gave Anna 480 beads
She gave Zoe 240 beads
------------------------------
check:
(3) +b+%2B+n+=+%281%2F2%29%2A%28++a+%2B+n+%29+
(3) +120+%2B+120+=+%281%2F2%29%2A%28++360+%2B+120+%29+
(3) +240+=+%281%2F2%29%2A480+
(3) +480+=+480+
OK