SOLUTION: a student has a x sweet. she gives 20 to her friends. if one-third of the reminder is equal to one-fifth of the original number of sweets, find the original number of sweets

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Question 1033508: a student has a x sweet. she gives 20 to her friends. if one-third of the reminder is equal to one-fifth of the original number of sweets, find the original number of sweets
Found 2 solutions by josmiceli, macston:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
She gives +20+ to friends
She has +x+-+20+ left
+%281%2F3%29%2A%28+x+-+20+%29+=+%281%2F5%29%2Ax+
Multiply both sides by +15+
+5%2A%28+x+-+20+%29+=+3x+
+5x+-+100+=+3x+
+2x+=+100+
+x+=+50+
There were originally 50 sweets
---------------
check:
+%281%2F3%29%2A%28+x+-+20+%29+=+%281%2F5%29%2Ax+
+%281%2F3%29%2A%28+50+-+20+%29+=+%281%2F5%29%2A50+
+%28+1%2F3+%29%2A30+=+%281%2F5%29%2A50+
+10+=+10+
OK

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
%281%2F3%29%28x-20%29=x%2F5 . Multiply each side by 3
.
x-20=3x%2F5 . Multiply each side by 5
.
5x-100=3x . Subtract 3x from each side
.
2x-100=0 . Add 100 to each side
.
2x=100 Divide each side by 2
.
x=50
.
ANSWER: The original number of sweets was 50.
.
CHECK:
.
%281%2F3%29%2850-20%29=%281%2F5%29%2850%29
.
1%2F3%2830%29=10
.
10=10
.