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jeka57 [31]
3 years ago
10

A clipboard costs $2.23. It costs $0.58 more than a notebook. Sheila bought two clipboards and one notebook. She paid with a ten

-dollar bill. How much change does sheila get? Use a tape diagram ti show

Mathematics
2 answers:
frozen [14]3 years ago
6 0

Sheila gets a change of \fbox {\begin\ \bf \$ 3.89\\\end{minispace}} when she pays a ten-dollar bill for two clipboards and a notebook.

Further explanation:

The cost of a clipboard is \$\ 2.23.

Also, it is given that the clipboard cost \$\text{ }0.58 more than a notebook so the cost of notebook is calculated as,

\fbox {\begin\\\\\begin{aligned}\text{Cost of a notebook}&= 2.23-0.58\\&=1.65\end{aligned}\end{minispace}}

Sheila bought two clipboards and one notebook then the total cost of items bought is taken as the sum of cost of two clipboard and cost of one notebook.

\fbox {\begin\\\\\begin{aligned}\text{Total cost of two clipboard and one notebook}&= 2.23+2.23+1.65\\&=6.11\end{aligned}\end{minispace}}

Sheila paid a ten dollar bill for the purchase of two clipboard and one notebook, so the total change she should get back is obtained as the difference of total cost of two clipboard and one notebook from the total paid price.

The tape diagram for the price paid for two clipboards and one notebook that sheila bought is as shown in Figure 1 (attached at the end).

Therefore, the change that Sheila gets back is calculated as,

\boxed{\begin{aligned}\text{Change that Sheila gets}&= 10-6.11\\&=3.89\end{aligned}}

Thus, the change amount that Sheila gets after she paid ten dollar for two clipboard and one notebook is \fbox {\begin\ \bf \$ 3.89\\\end{minispace}}.

Learn more:

1. Fractional expression simplification brainly.com/question/894273

2.  Linear equation application brainly.com/question/2479097

3. Composite functions brainly.com/question/2142762

Answer details  

Grade: Middle school  

Subject: Mathematics  

Chapter: Simplification

Keywords: notebook, clipboard, ten-dollar bill, paid, costs, Sheila, bought, $2.23, $0.58, $4.46, change amount, total cost, amount, two clipboards.

Troyanec [42]3 years ago
3 0
Hey! So, you know she bought two clipboards. You're going to want to add 2.23 and 2.23 together, which is 4.46. Sheila only bought one notebook, so you simply add 4.46 and 0.58 together, which is 5.05. But, wait! She paid with a 10 dollar bill. Now, we have to take 5.05 out of 10.00, which is 4.95. Now, our answer is going to be $4.95 in change. I hope I helped! :)
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\large \bigstar \frak{ } \large\underline{\sf{Solution-}}

Consider, LHS

\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}

We know,

\begin{gathered}\boxed{\sf{  \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered}  \\  \\  \text{So, using this identity, we get} \\  \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}

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\begin{gathered}\boxed{\sf{  \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered}  \\

So, using this identity, we get

\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}

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\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\  \\  \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\  \\  \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\  \\  \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\  \\  \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}

<h2>Hence,</h2>

\begin{gathered} \\ \rm\implies \:\boxed{\sf{  \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}

\rule{190pt}{2pt}

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