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MrRa [10]
3 years ago
7

A student has 10 coins in her pocket that have a value of 0.85,The coins are either nickels of dimes. Which system of linear equ

ations represents this scenario?
Mathematics
1 answer:
oee [108]3 years ago
7 0

Answer:

p+q = 10...... 1

0.05p+0.10q = 0.85 ..... 2

Step-by-step explanation:

The question is incomplete. Here is the complete question.

A student has 10 coins in her pocket that have a value of $0.85. The coins are either nickels or dimes. If each nickel costs $0.05 and each dime costs $0.10. Which system of linear equations represents this scenario?

Let the number of nickel in the pocket of the student be p

Let the number of dime in the pocket of the student be q

If there are 10 coins in her pocket, then the total coins in her pocket will be represented by the equation;

p+q = 10...... 1

If each nickel costs $0.05, p nickels will cost $0.05×p = $0.05p

If each dime costs $0.10, q nickel will costs $0.10×q = $0.10q

Total amount will be $0.05p+$0.10q

Now if the total coins in her pocket has a value of $0.85, then the we will equate $0.05p+$0.10q to $0.85 to give our second linear equation as:

$0.05p+$0.10q = $0.85 ....... 2

Therefore, the system of linear equations represents this scenario are:

p+q = 10...... 1

0.05p+0.10q = 0.85 ..... 2

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I made my own graph using the given points. Pls. see attachment. 

<span>Part A: Using the graph above, create a system of inequalities that only contains points D and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.

I used paint program to graph the points based on the given data. 
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The yellow lines above represents the shaded portion of the graph.

y = mx + b

b is the y-intercept. It is the value of y when x is 0. In this case, b = 3.5
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Part B: Explain how to verify that the points D and F are solutions to the system of inequalities created in Part A.

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y ≥ 1/4x + 3.5

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<span>
Part C: Chickens can only be raised in the area defined by y > 2x − 2. Explain how you can identify farms in which chickens can be raised.

y > 2x - 2

We will get the coordinates of each point and see if its x value will generate the desired value of y.

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