You can solve this problem by creating a system of equations and solving by substitution. This allows you to solve for one of the unknown values (in this case, the number of short answer and number of multiple choice) and you can then solve for both, if you would like.
The two variables in your equations standing in for these missing values represent the number of short answer (s) and the number of multiple choice questions (m).
First create an equation for the number of total questions on the test. The total number of multiple choice and short answer questions is 45:
m + s = 45
Then create an equation with these variables representing the number of points on the test. The point values for each question will be the variable coefficients (numbers that the variables are multiplied by in this problem).
2m + 5s = 120
Now you can take the first equation - since it is simpler, the variables don't have coefficients so it only requires subtraction to get one variable by itself - solve for one of the variables, and substitute the result into the second equation in place of that variable. You will then be able to solve for that variable!
First, solve for m in the first equation by moving the m to one side of the equals sign by itself. It then becomes 45 - s = m
Now put (45-s) into the second equation in place of m.
120 = 2(45-s) + 5s
Distribute the 2(45-s)
120 = 90 - 2s + 5s
Add the "s" expressions together. Subtract 90 from both sides.
30 = 3s
Divide by 3 and find that s = 10
There are 10 short answer questions on the test.
For Point P, you need to recognize that a 1:2 ratio means that AP will be 1/3 of AB and PB will be 2/3 of AB.
So you need to find the change in the x-values, 14-2 = 12, and then add 1/3 of that change to the x-value of A.
Then you need to find the change in the y-values, 9-3 = 6, and then add 1/3 of that change to the y-value of A.
For the bisector, that's another way to say you'll split AB into two even pieces. For this, it's the same as what we just did, but you need to find 1/2 of the two respective changes (1/2 of the x-change and 1/2 the y-change).
Answer:
(-2,0) and (-4,-2)
Step-by-step explanation:
The solution to the system of equations is where the two graphs cross
They cross at (-2,0) and (-4,-2)
1000+1500=2500 is how much she owes right now
If each hat is sold for 12.50, all you have to do is 2500/12.50=200
She needs to sell 20 hats to break even.
