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3 years ago

Seven times a number is equal to 12 more than 3 times the number. find the number.

Mathematics

1 answer:

ankoles [38]3 years ago

3 0

Answer:

the number is 3

Step-by-step explanation:

seven times a number is equal to 12 more than 3 times the number

7*n = 12+3*n

7n=12+3n

subtract 3n from each side

7n-3n = 12+3n-3n

4n = 12

divide each side by 4

4n/4 = 12/4

n =3

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Answer:

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Step-by-step explanation:

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3 years ago

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3 years ago

Pauline, Patricia and Polly are pie bakers at their bakery, Perfect Pies. They bake four different pie flavors: cherry, blueberr

Shkiper50 [21]

Answer:

The answer is given below

Step-by-step explanation:

1) The persons are given by the matrix:

The number of different pie flavours is given by the matrix:

$n=\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right]$

The cost of ingredients for each pie is given by the matrix:

$I=\left[\begin{array}{ccc}3\\5\\2\\6\end{array}\right]$

$\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}3\\5\\2\\6\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}37\\92\\50\end{array}\right]$

3) The cost of pie for Patricia = $92

The total cost of pie for all bakers = 37 + 92 + 50 = $179

The ratio of cost of Patricia pie to that of all three bakers = $92/$179 = 0.514

Patricia pie cost of ingredients is more than half of that of all three bakers

The price of pie at Samuels sweet is represented by the matrix:

$SA=\left[\begin{array}{ccc}8\\10\\7\\12\end{array}\right]$

The income of each baker made by selling at samuels sweets is:

$\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}8\\10\\7\\12\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}83\\208\\119\end{array}\right]$

The price of pie at Sugary Sarah is represented by the matrix:

$SS=\left[\begin{array}{ccc}8\\9\\8\\13\end{array}\right]$

The income of each baker made by selling at Sugary Sarah is:

$\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{cccc}3&4&1&1\\6&6&4&6\\2&2&5&4\end{array}\right] \left[\begin{array}{ccc}8\\9\\8\\13\end{array}\right] \\\left[\begin{array}{ccc}Pauline\\Patricia\\Polly\end{array}\right] =\left[\begin{array}{ccc}81\\212\\126\end{array}\right]$

5) Patricia yielded the greatest income. She made $208 + $212 = $420

6) Polly made $126 from selling at Sugary Sarah

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3 years ago