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Bumek [7]
2 years ago
9

Julio bought 4 pencils and 3 erasers for $0.37 and David paid $0.33 for 3 pencils and 4 erasers. What is the cost of one pencil?

What is the cost of one eraser?
Mathematics
1 answer:
nirvana33 [79]2 years ago
7 0

Answer:

Each pencil costs $0.07 and each eraser costs $0.03

Step-by-step explanation:

System of linear equations

It refers to the study of systems when n variables are related in m linear equations, each one is not independent from the others. Solving such systems can be done following very diverse approaches.  

Let p=the price of each pencil while e is the price each eraser

Julio bought 4 pencils and 3 erasers, spending

4p+3e=0.37

David bought 3 pencils and 4 erasers, spending

3p+4e=0.33

The system of equations is written in the form

\left\{\begin{matrix}4p+3e=0.37\\ 3p+4e=0.33\end{matrix}\right

We'll solve it by reduction. Multiplying the first equation by -3 and the second by 4:

\left\{\begin{matrix}-12p-9e=-1.11\\ 12p+16e=1.32\end{matrix}\right.

Adding both equations:

7e=0.21  

e=0.03

Multiplying the first one by -4 and the second by 3

\left\{\begin{matrix}-16p-12e=-1.48\\ 9p+12e=0.99\end{matrix}\right.\end{matrix}\right.

Adding both equations:

-7p=-0.49

p=0.07  

Solution: Each pencil costs $0.07 and each eraser costs $0.03

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Step-by-step explanation:

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He spent  \frac{3}{8} on food i.e.

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\dfrac{1}{6}\ \text{on other expenses i.e.}\\\\\Rightarrow \dfrac{1}{6}\times 2400=\$400

Remaining money = 2400-900-800-400=\$300

So, he saved $300 after expenses

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Which set of ordered pairs ***represents*** a function?
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100 POINTS TO RIGHT AWNSER!!!!
makvit [3.9K]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/3000586

——————————

The answer is option D)  r < 5  or  r > – 1.

I'm going to graph each inequality below on a number line.


A)  r > 5  or  r > – 1.

\large\begin{array}{cl} \mathsf{r>5}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\textsf{|||||}\!\!\underset{5}{\circ}\!\!\overset{*****~~~}{\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\ \mathsf{r>-1}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\overset{********************~~~}{\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\\\ \mathsf{r>5~~or~~r>-1}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\overset{********************~~~}{\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}} \end{array}

The result is found just by joining those two intervals together. Actually that compound inequality only implies

r > – 1

which does not represent all real numbers.

—————

B)  r > 5  or  r < – 1.

\large\begin{array}{cl} \mathsf{r>5}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\textsf{|||||}\!\!\underset{5}{\circ}\!\!\overset{*****~~~}{\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\ \mathsf{r5~~or~~r

Numbers between – 1  and  5 (including them) are not included in the union, so you don't have all real numbers represented there either.

—————

C)  r < 5  or  r < – 1.

\large\begin{array}{cl} \mathsf{r

Numbers that are greater or equal to 5 are not in the union. So it does not represent all real numbers.

—————

D)  r < 5  or  r > – 1.

\large\begin{array}{cl} \mathsf{r-1}&\qquad\mathsf{\textsf{|||}\!\!\!\underset{-1}{\circ}\!\!\!\overset{********************~~~}{\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}}\\\\\\ \mathsf{r-1}&\qquad\mathsf{\overset{~~~**************************~~~}{\textsf{|||}\!\!\!\underset{-1}{\bullet}\!\!\!\textsf{|||||}\!\!\underset{5}{\bullet}\!\!\textsf{|||}}\!\!\!\footnotesize\begin{array}{l}\blacktriangleright \end{array}\qquad \mathbb{R}} \end{array}

Now all real numbers are included in the union. So this is the right choice.


Answer:  option D)  r < 5  or  r > – 1.


I hope this helps. =)

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Explanation:

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