Not including tax, a total of 19 pens and markers cost $11.50. The pens cost $0.25 each, and the markers cost $0.75 each. Write the system of equations that could be used to solve for the number of pens, p, and the number of markers, m, bought.(4 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. p + m =
19
Based on the given information, the first equation that can be formed is:
p + m = 19
Next, let's consider the cost of the pens and markers.
The cost of each pen is $0.25, so the total cost of pens can be represented as:
0.25p
Similarly, the cost of each marker is $0.75, so the total cost of markers can be represented as:
0.75m
According to the given information, the total cost of pens and markers is $11.50, which can be represented as:
0.25p + 0.75m = 11.50
Hence, the system of equations that can be used to solve for the number of pens and markers bought is:
p + m = 19
0.25p + 0.75m = 11.50
p + m = 19
p + m = 19
Joyce wants to go to the zoo with her friend over spring break. You can pay $45 to get into the zoo each time, or join a membership for $50 and then only pay $20 each visit to the zoo. How many times will Joyce need to visit the zoo to justify the expense of the membership fee?(1 point) Responses 3 3 5 5 10 10 2
Let's assume Joyce needs to visit the zoo x number of times to justify the expense of the membership fee.
If Joyce decides to pay the regular entrance fee each time, the cost would be $45 per visit. So the total cost without the membership would be 45x.
If Joyce decides to get the membership, she would need to pay an initial fee of $50 and then $20 per visit. So the total cost with the membership would be 50 + 20x.
To justify the expense of the membership fee, the total cost without the membership should be equal to the total cost with the membership:
45x = 50 + 20x
Subtracting 20x from both sides:
25x = 50
Dividing both sides by 25:
x = 2
Therefore, Joyce would need to visit the zoo 2 times to justify the expense of the membership fee.
Two systems of equations are shown: 4x+y=−1 x+y=2 and 8x+2y=−2 −4x+cy=−8 What would the value of c need to be to get the same solution for both systems? (1 point) Responses 1 1 -4 -4 4 4 2 2 -2
To get the same solution for both systems, the two systems of equations must be equivalent.
For the first system of equations:
4x + y = -1
x + y = 2
If we multiply the second equation by 4, we get:
4(x + y) = 4(2)
4x + 4y = 8
Now, let's compare this equation to the second system of equations:
8x + 2y = -2
-4x + cy = -8
To make the two systems equivalent, the coefficients of the x and y terms should be the same.
Comparing the x terms:
8x = 4x
8x - 4x = 0
This implies that the coefficient of x in the second system is 4.
Comparing the y terms:
2y = cy
2y - cy = 0
When the coefficients of y are equal, the value of c does not matter.
Therefore, the value of c can be any number.