SOLUTION: Box A has 128 apples more than Box B. Marcus moved 25% of the apples from Box A to Box B. Then, he moved 1/8 of the apples in Box B to an empty Box C. In the end, Box C had 1

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Box A has 128 apples more than Box B. Marcus moved 25% of the apples from Box A to Box B. Then, he moved 1/8 of the apples in Box B to an empty Box C. In the end, Box C had 1      Log On


   



Question 1078361: Box A has 128 apples more than Box B.
Marcus moved 25% of the apples from Box A to Box B.
Then, he moved 1/8 of the apples in Box B to an empty Box C.
In the end, Box C had 149 apples less than the remaining apples in Box A.
A. Find the number of apples in Box C
B. Find the number of apples in Box A at first.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a, b, and c+ = the
number of apples in the respective boxes
at the 1st step
-----------------------
step 1
A has +a+=+b+%2B+128+
B has +b+
C has +c+=+0+
-------------------------
step 2
A has +a+-+.25a+=+.75a+
+.75a+=+.75%2A%28+b+%2B+128+%29+
B has +b+%2B+.25%2A%28+b+%2B+128+%29+
+1.25b+%2B+32+
C has +c+=+0+
-----------------------------
step 3
A has +.75a+=+.75%2A%28+b+%2B+128+%29+
B has +%287%2F8+%29%2A%28+1.25b+%2B+32+%29+
C has +%281%2F8%29%2A%28+1.25b+%2B+32+%29+
------------------------------
After this step,
+%281%2F8%29%2A%28+1.25b+%2B+32+%29+=+%283%2F4%29%2A%28+b+%2B+128+%29+-149+
Multiply both sides by +8+
+1.25b+%2B+32+=+6%2A%28+b+%2B+128+%29+-+1192+
+1.25b+%2B+32+=+6b+%2B+768+-+1192+
+4.75b+=+1192+%2B+32+-+768+
+4.75b+=+456+
+b+=+96+
-----------------------------
A.
The number of apples in box C is
C has +%281%2F8%29%2A%28+1.25b+%2B+32+%29+
+%281%2F8%29%2A%28+1.25%2A96+%2B+32+%29+
+%281%2F8%29%2A%28+120+%2B+32+%29+
+%281%2F8%29%2A152+=+19+
C has 19 apples at the end
------------------------------
B.
Find a, the original number of apples in box A
step 3
A has +.75a+=+.75%2A%28+b+%2B+128+%29+
+.75a+=+.75%2A%28+96+%2B+128+%29+
+.75a+=+.75%2A224+
+a+=+224+
There were 224 apples in box A to start with
===================================
check the answers:
1st step:
+a+=+b+%2B+128+
+a+=+96+%2B+128+
+a+=+224+
+b+=+96+
+c+=+0+
--------------------
2nd step:
+.75a+=+.75%2A224+
+.75a+=+168+
and
+1.25b+=+1.25%2A96+
+1.25b+=+120+
and
+c+=+0+
---------------------
3rd step:
A has:
+.75a+=+168+
and
B has:
+%287%2F8+%29%2A%28+1.25b+%2B+32+%29+
+%287%2F8+%29%2A%28+1.25%2A96+%2B+32+%29+
+%287%2F8%29%2A%28+120+%2B+32+%29+
+%287%2F8%29%2A152+=+133+
and
C has:
+%281%2F8%29%2A%28+1.25b+%2B+32+%29+
+%281%2F8%29%2A%28+1.25%2A96+%2B+32+%29+
+%281%2F8%29%2A152+=+19+
------------------------------
The totals must be the same at
start and finish
+a+=+224+
+b+=+96+
+c+=+0+
Total = 320
-----------------
After step C:
+a+=+168+
+b+=+133+
+c+=+19+
Total = 320
OK