Sarika sells to the first customer half her stock and half her coconuts to the second customer she sells half her remaining stock and half a coconut and so on to the third and fourth customer. 15 coconuts are left with her now. How many coconuts did she have before she started selling?
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Step-by-step explanation:
Suppose she had x apples in the beginning.
Sold to the first customer =
2
x
+
2
1
=
2
x+1
Remaining stock =x−
2
x+1
=
2
2x−x−1
=
2
x−1
Sold to the second customer =
2
1
×
2
x−1
+
2
1
=
4
x−1
+
2
1
=
4
x−1+2
=
4
x+1
Remaining stock =(
2
x−1
)−(
4
x+1
)=
4
2x−2−x−1
=
4
x−3
Sold to the third customer
2
1
×
4
x−3
+
2
1
=
8
x−3
+
2
1
=
8
x−3+4
=
8
x+1
Remaining sock =(
4
x−3
)−(
8
x+1
)=
8
2x−6−x−1
=
8
x−7
Sold to the fourth cutomer =
2
1
×
8
x−7
+
2
1
=
16
x−7
+
2
1
=
16
x−7+8
=
16
x+1
Therefore, x−[
2
x+1
+
4
x+1
+
8
x+1
+
16
x+1
]=15
⇒x−[
16
8x+8+4x+4+2x+2+x+1
]=15
⇒x−[
16
15x+15
]=15
⇒
16
16x−15x−15
=15⇒x−15=16×15=240
⇒x=240+15=255
Therefore, she had 255 apples before she
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