Your teacher is giving you a test worth 100 points containing 40 questions. There are two-point and four-point questions on the test. How many of each type of question are on the test?

How would you set this up?

Suppose there are x 2-pointers and y 4-pointers.

x + y = 40

2x + 4y = 100

If you are learning algebra, you probably know what to do next.

You could double both sides of the first equation and subtract what you get from the second equation, for example. That would give you 2y = 20 right away.

Ok you have to write a system of equations.

x+y=40
2x+4y=100

y=40-x

2x+4(40-x)=100

solve: X=30 Y=10

then 30+y = 40
y=10

I totally understand now! i had the 2x+4y=100...i just was blanking out about how to set up the 2nd part but I see now! Thank you so much! :)

what is the fraction lowes terms and a decimal 54

X-y=5

4x+6y=120

Thanks

To solve this problem, we need to set up a system of equations based on the given information. Let's assume the number of two-point questions is represented by the variable 'x', and the number of four-point questions is represented by the variable 'y'.

From the information given, we know that there are a total of 40 questions on the test. So, our first equation will be:

x + y = 40

We also know that the total score of the test is 100 points. Since each two-point question contributes 2 points and each four-point question contributes 4 points, our second equation will be:

2x + 4y = 100

Having established these two equations, we can now solve them simultaneously to find the values of 'x' and 'y'. There are multiple methods to solve this system of equations, such as substitution or elimination.

Let me know if you would like me to walk you through solving the equations using either of these methods.