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.
Answer: Write something greater than 5 at the ones place or the tenths place or having digits that are greater than 0 after the 5 in the tenths place.
Step-by-step explanation:
The equation would be y = 25x + 50
In order to find this equation, we need to know how much the gift from her grandparents was. To do so, we have to find out how much she's saved from dog walking.
Since she saves $25 a month for 7 months, we can find the total amount as:
25*7 = 175
Then we can subtract that from the total she has saved to find the amount for the gift.
225 - 175 = 50
Finally, we put the amount per month in the equation with the gift as the y intercept to create the equation above.
Slope formula = y=mx+b
2x+4y=12
Minus 2x from both sides
4y= -2x+12
Divide 4 from both sides
Y= -1/2x + 4
Hope this helps!
Our equation: 33x + 10 = 5 - 2x
Step 1:
To solve for x, we need to remember to isolate the variable (that is our way to solve for x). To do that, we add 2x on the right side of the equation to cancel -2x out. Then, we add 2x on the left of the equation. The equation becomes:
Step 2:
We subtract 10 from both sides (to cancel out the 10 on the left). Equation:
Step 3: Divide 35 on both sides to get our x value.
Answer: 
Hope this helps!
