guys plzzzz plzz answer fast this question
Answers
Answer:
Sold to the first customer
\begin{gathered}\frac{x}{2} + \frac{1}{2} = \frac{x + 1}{2} \\\end{gathered}
2
x
+
2
1
=
2
x+1
Remaining stock
\begin{gathered}= x - \frac{x + 1}{2} = \frac{2x - x - 1}{2} \\ = \frac{x - 1}{2}\end{gathered}
=x−
2
x+1
=
2
2x−x−1
=
2
x−1
Sold to the second customer
\begin{gathered}= \frac{1}{2} \times \frac{x - 1}{2} + \frac{1}{2} \\ = \frac{x - 1}{4} + \frac{1}{2}\end{gathered}
=
2
1
×
2
x−1
+
2
1
=
4
x−1
+
2
1
= \frac{x - 1 + 2}{4} = \frac{x + 1}{4}=
4
x−1+2
=
4
x+1
Remaining stock
\begin{gathered}= ( \frac{x - 1}{2}) - ( \frac{x + 1}{4} ) \\ = \frac{2x - 2 - x - 1}{4} \\ = \frac{x - 3}{4}\end{gathered}
=(
2
x−1
)−(
4
x+1
)
=
4
2x−2−x−1
=
4
x−3
Sold to the third customer
\begin{gathered}= \frac{1}{2} \times \frac{x - 3}{4} + \frac{1}{2} \\ = \frac{x - 3 + 4}{8} \\ = \frac{x + 1}{8}\end{gathered}
=
2
1
×
4
x−3
+
2
1
=
8
x−3+4
=
8
x+1
Remaining stock
\begin{gathered}= ( \frac{x - 3}{4} ) - ( \frac{x + 1}{8} ) \\ = \frac{2x - 6 - x - 1}{8} = \frac{x - 7}{8}\end{gathered}
=(
4
x−3
)−(
8
x+1
)
=
8
2x−6−x−1
=
8
x−7
Sold to the fourth customer
\begin{gathered}= \frac{1}{2} \times \frac{x - 7}{16} + \frac{1}{2} \\ = \frac{x - 7}{16} + \frac{1}{2} \\ = \frac{x - 7 + 8}{16} \\ = \frac{x + 1}{16}\end{gathered}
=
2
1
×
16
x−7
+
2
1
=
16
x−7
+
2
1
=
16
x−7+8
=
16
x+1
Therefore,
\begin{gathered}x - ( \frac{x + 1}{2} + \frac{x + 1}{4} + \frac{x + 1}{8} + \frac{x + 1}{16} ) \\ = 15\end{gathered}
x−(
2
x+1
+
4
x+1
+
8
x+1
+
16
x+1
)
=15
\begin{gathered}= > x - ( \frac{8x + 8 + 4x + 4 + 2x + 2 + x + 1}{16} ) \\ = 15\end{gathered}
=>x−(
16
8x+8+4x+4+2x+2+x+1
)
=15
\begin{gathered}= > x - ( \frac{15x + 15}{16} ) = 15 \\ = > \frac{16 x - 15x - 15}{16} \\ = 15 \\ = > x - 15 = 16 \times 15 = 240 \\ = > x = 240 + 15 = 255.\end{gathered}
=>x−(
16
15x+15
)=15
=>
16
16x−15x−15
=15
=>x−15=16×15=240
=>x=240+15=255.