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3 years ago

Read the problem and answer the questions show your solution when necessary.

Mathematics

1 answer:

Alexandra [31]3 years ago

4 0

Answer:

Step-by-step explanation:

1) Number of white chocolate bars = x

Number of dark chocolate bars = y

Total bars = 15

x + y = 15 --------------(I)

Total cost = Php. 340

20x + 25y = 340 ----------------(II)

2) We can use elimination method to solve this equations.

Multiply equation (I) by (-20) and then add the equations.

(I)* (-20) -20x -20y = - 300

(II) <u>20x + 25y = 340 </u> {Now add and x will be eliminated}

5y = 40

y = 40/5

y = 8

Substitute y = 8 in equation (I)

x + 8 = 15

x = 15 - 8

x = 7

3) Number of dark chocolate bars = 8

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3 years ago

Use the augmented matrix method to solve the following system of equations. Your answers may be given as decimals or fractions.

Alexandra [31]

Answer:

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

Step-by-step explanation:

Given equations are

x - 2y - z = 2

x + 3y - 2z = 4

-x + 2y + 3z = 2

from the given equations the augmented matrix can be written as

$\left[\begin{array}{ccc}1&-2&-1:2\\1&3&-2:4\\-1&2&3:2\end{array}\right]$

$R_2=>R_2-R_1\ and\ R_3=>R_3+R_1$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&5&-1:2\\0&0&2:4\end{array}\right]$

$R_2=>\dfrac{R_2}{5}$

$=\ \left[\begin{array}{ccc}1&-2&-1:2\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\0&0&2:4\end{array}\right]$

$R_1=>R_1+2.R_2$

$=\ \left[\begin{array}{ccc}1&0&-1-\dfrac{2}{5}:2+\dfrac{4}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&2:4\end{array}\right]$

$R_3=>\dfrac{R_3}{2}$

$=\ \left[\begin{array}{ccc}1&0&\dfrac{-7}{5}:\dfrac{14}{5}\\\\0&1&\dfrac{-1}{5}:\dfrac{2}{5}\\\\0&0&1:2\end{array}\right]$

$R_1=>R_1+\dfrac{7}{5}R_3\ and\ R_2+\dfrac{1}{5}R_3$

$=\ \left[\begin{array}{ccc}1&0&0:\dfrac{14}{5}+\dfrac{7}{5}\\\\0&1&0:\dfrac{2}{5}+\dfrac{1}{5}\\\\0&0&1:2\end{array}\right]$

So, from the above augmented matrix, we can write

$x\ =\ \dfrac{21}{5}$

$y\ =\ \dfrac{3}{5}$

z = 2

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3 years ago

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Step-by-step explanation:

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3 years ago

Read the problem and answer the questions show your solution when necessary. ​

Read the problem and answer the questions show your solution when necessary.