Question

To determine the number of problems of each value on the test, you can set up a system of equations based on the given information. Let x be the number of questions worth 2 points and y be the number of questions worth 4 points. You have two pieces of information: x + y = 35 (total number of problems) 2x + 4y = 100 (total points on the test) Now, you can solve this system of equations to find the values of x and y.

Answer 1

You're on the right track! You've correctly set up a system of equations based on the given information.

Now, let's solve this system of equations to find the values of x and y.

Here's the system of equations you have:

1. x + y = 35 (total number of problems)

2. 2x + 4y = 100 (total points on the test)

Let's use the first equation (x + y = 35) to express x in terms of y:

x = 35 - y

Now, substitute this expression for x into the second equation (2x + 4y = 100):

2(35 - y) + 4y = 100

Now, distribute and simplify:

70 - 2y + 4y = 100

Combine like terms:

2y = 100 - 70

2y = 30

Now, divide by 2 to solve for y:

y = 30 / 2

y = 15

So, you've found that y, the number of questions worth 4 points, is 15.

Now, you can use this value to find x, the number of questions worth 2 points, using the first equation:

x + 15 = 35

Subtract 15 from both sides:

x = 35 - 15

x = 20

So, you've found that x, the number of questions worth 2 points, is 20.

Therefore, there are 20 questions worth 2 points and 15 questions worth 4 points on the test.