The math club sold slices of pizza p at a profit of three dollars each and cans of soda s at two dollars each Troy’s money for a trip they sold 200 items they made a profit of 550. Write the pair of linear equations that model the situation.
Equations to represent the total number of items sold blank equals 200
Equation to represent the total profit blank equals 550
Let's represent the total number of pizza slices sold as p and the total number of cans of soda sold as s.
1. Equation for the total number of items sold:
p + s = 200
2. Equation for the total profit:
3p + 2s = 550
The Lakewood baseball team is selling T-shirts for a fundraiser. The T-shirts cost $100 for the printing design and set up plus $10 per shirt. The team is going to sell the shirts for 15 each. How many shirts do they need to sell to break even
Blank shirts
Let's represent the number of shirts they need to sell to break even as x.
The cost equation would be:
Cost = $100 (design and set up) + $10 (cost per shirt) * x (number of shirts)
The revenue equation would be:
Revenue = $15 (selling price per shirt) * x (number of shirts)
To break even, the cost and revenue should be equal:
Cost = Revenue
$100 + $10x = $15x
Simplifying the equation:
$10x - $15x = -$100
-$5x = -$100
Dividing both sides by -5:
x = 20
Therefore, they need to sell 20 shirts to break even.
The Kingsley middle school PTA is planning a carnival to raise money for the schools are department they estimate that the event will be very popular and they will have 500 people attend. They plan to charge adults $10 and children five dollars for admission the PTA wants to earn 3500 from administration charges how many adults and how many children need to attend for the PTA to raise their goal of 3500.
Let's represent the number of adults attending as A and the number of children attending as C.
The total number of people attending would be:
A + C = 500
The revenue equation would be:
Revenue = $10 (adult admission) * A (number of adults) + $5 (child admission) * C (number of children)
To raise $3500 in revenue:
Revenue = $3500
Therefore, we have the following system of equations:
A + C = 500
$10A + $5C = $3500
To solve this system of equations, we can use substitution or elimination method.
Let's solve using substitution method:
From the first equation, we can express A in terms of C:
A = 500 - C
Substitute this value of A in the second equation:
$10(500 - C) + $5C = $3500
Expanding and simplifying:
$5000 - $10C + $5C = $3500
-$5C = $3500 - $5000
-$5C = -$1500
Divide both sides by -5:
C = -$1500 / -5
C = 300
Now substitute the value of C in the first equation to find A:
A + 300 = 500
A = 500 - 300
A = 200
Therefore, the PTA needs 200 adults and 300 children to attend in order to raise their goal of $3500.
You are designing a simulation in which two characters moving along different paths are going to collide when the characters are at the same point at the same time. The position of the first character is given by Y equals 2T. And the second is Y equals T +2. Why is in centimeters and T is in time in seconds how many seconds after the simulation started with the characters collide?
To find the time at which the characters will collide, we need to set the y-values of the two characters equal to each other and solve for T.
For the first character: Y = 2T
For the second character: Y = T + 2
Setting these equal to each other:
2T = T + 2
Subtracting T from both sides:
2T - T = 2
Simplifying:
T = 2
Therefore, the characters will collide 2 seconds after the simulation started.
Solve the following system of linear equations by graphing graph on your own piece of paper in your submitted answer describe what the graph looks like and what this tells you about the solution to the system of linear equations
Y equals X +3
Negative 4X plus 4Y equals 28
To graph the system of linear equations, we need to graph each equation separately and then identify the point or points where the two lines intersect.
1. Graph the equation Y = X + 3:
To graph this equation, we start with the y-intercept, which is 3. From there, we use the slope of 1 (since the equation is in slope-intercept form, y = mx + b). So, for each unit we move to the right, we move up one unit. Plotting these points and connecting them, we get a line.
2. Graph the equation -4X + 4Y = 28:
To graph this equation, we can rearrange it to the slope-intercept form by solving for Y:
4Y = 4X + 28
Y = X + 7
Using the slope-intercept form, we plot the y-intercept at 7 and use the slope of 1, just like in the previous equation. Plotting the points and connecting them, we get another line.
Looking at the graph, we can see that the two lines intersect at the point (2, 5). This means that the x-coordinate of the intersection point is 2, and the y-coordinate is 5.
In terms of the solution to the system of linear equations, (2, 5) represents the values of x and y that satisfy both equations simultaneously. Therefore, the solution to the system of equations is x = 2 and y = 5.
To write the pair of linear equations that model the situation, we need to define variables for the number of slices of pizza and the number of cans of soda sold.
Let's say:
p = number of slices of pizza sold
s = number of cans of soda sold
Equation for the total number of items sold:
The total number of items sold is equal to the sum of the number of slices of pizza and the number of cans of soda.
Therefore, p + s = 200.
Equation for the total profit:
The profit from selling pizza slices is $3 each, so the total profit from selling p slices of pizza is 3p.
The profit from selling cans of soda is $2 each, so the total profit from selling s cans of soda is 2s.
Therefore, the total profit is 3p + 2s = 550.
Thus, the pair of linear equations that model the situation is:
p + s = 200 (Equation 1)
3p + 2s = 550 (Equation 2)