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True [87]
2 years ago
5

If a pen and a pencil cost 1.10$ but the pen cost is 1$ more than pencil​

Mathematics
1 answer:
Stella [2.4K]2 years ago
4 0

Answer:

The pencil cost $0.05 and the pen cost $1.05.

Step-by-step explanation:

Let, the price of the pencil is $ .

Given that the pen costs a dollar more than the pencil,

So, the price of the pen=$+1.

Therefore, ++1=1.10

, 2+1=1.10

, 2=1.10–1

, 2=0.10

, =0.10/2

, =0.05

The pencil cost $0.05 and the pen cost $1.05.

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The table shows the number of books donated to a library each month. Suppose the growth continues exponentially.
telo118 [61]
\bf \begin{array}{ccll}
\stackrel{t}{months}&\stackrel{A}{books}\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
0&80\\
1&100\\
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\end{array},    we know that on Month 0, the Books were 80

\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &80\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &0\\
\end{cases}
\\\\\\
80=I(1+r)^0\implies 80=I\qquad therefore\qquad \boxed{A=80(1+r)^t}

we also know that on the first month there were 100 books,

\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &100\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\to &1\\
\end{cases}
\\\\\\
100=80(1+r)^1\implies \cfrac{100}{80}=1+r\implies \cfrac{5}{4}=1+r
\implies 
\cfrac{5}{4}-1=r
\\\\\\
 \cfrac{1}{4}=r\implies 0.25=r\qquad therefore\qquad \boxed{A=80(1+0.25)^t}

now, how many books when t = 8?   A=80(1+0.25)⁸, or A=80(1.25)⁸.
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