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horsena [70]
3 years ago
9

8

Mathematics
1 answer:
marissa [1.9K]3 years ago
3 0

Answer:

11 pennies

33 nickels

7 quarters

Step-by-step explanation:

Let x be the number of pennies, then the number of nickels is 3x.

There are 51 coins in total, so the number of quarters is 51 - x - 3x = 51 - 4x.

Amounts:

  • in pennis - x cents;
  • in nickels - 5(3x) = 15x cents;
  • in quarters - 25(51 - 4x) cents.

Tota amount = $3.51 = 351 cents.

Hence,

x+15x+25(51-4x)=351\\ \\x+15x+1,275-100x=351\\ \\x+15x-100x=351-1,275\\ \\-84x=-924\\ \\84x=924\\ \\ x=11

11 pennies

33 nickels

7 quarters

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Anna71 [15]

Considering the given system of equations, it is found that:

|Ay| = \left|\begin{array}{cc}-8&1\\-6&-1\end{array}\right|

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the system is:

-8x+y=-6

3x-2y=-1

In matrix form, it is given by:

\left[\begin{array}{cc}-8&1\\3&-2\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-6\\-1\end{array}\right]

To find the matrix |Ay|, we replace the y coefficients of 1 and -2 by the results of -6 and -1, hence:

|Ay| = \left|\begin{array}{cc}-8&1\\-6&-1\end{array}\right|

More can be learned about a system of equations at brainly.com/question/24342899

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2 years ago
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Answer:

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Step-by-step explanation:

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Follow the steps to finish solving the equation –3x + 18 = 7x.
RSB [31]

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3 years ago
after 12 girls left the school assembly the ratio of the number of boys to girls is 3 to 4. if there were w boys at the assembly
son4ous [18]
Let g = original # of girls at the assembly.
Let w = # of boys at the assembly.

Equation of ratios:

w                 3         boys
-------    =    ---- = --------------------------------------------
g-12             4      girls after 12 have left assembly
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This is "original # of girls at the assembly in terms of w, the # of boys at the assembly."
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