Question

Which of the following systems of equations could be used to determine f, the number of five-point questions, and t, the number of two-point questions?

A. 5f + 2t = 130
B. 2f + 5t = 130
C. f + t = 50
D. 5f + 2t = 50

Answer 1

The correct system of equations to determine the number of five-point questions (f) and the number of two-point questions (t) is option A: 5f + 2t = 130. To solve this system of equations, you can use the substitution method to find the values of f and t.

Step-by-step explanation:

The correct system of equations to determine the number of five-point questions (f) and the number of two-point questions (t) is option A: 5f + 2t = 130.

To solve this system of equations, you can use a variety of methods, such as substitution, elimination, or graphing. Let's use the substitution method:

1. First, solve one equation for one variable in terms of the other variable. From equation 1, isolate f: f = (130 - 2t)/5.
2. Next, substitute this value of f into the second equation: 2f + 5t = 130.
3. Replace f with (130 - 2t)/5 in the second equation: 2((130 - 2t)/5) + 5t = 130.
4. Simplify and solve for t: 260/5 - 4t/5 + 5t = 130.
5. Combine like terms and solve the resulting equation: 260 - 4t + 25t = 650.
6. Combine like terms again: 21t = 390.
7. Divide both sides by 21 to solve for t: t = 18.57.

So, the number of two-point questions (t) is approximately 18.57. Now, substitute this value of t into either of the original equations to solve for f: f = (130 - 2(18.57))/5 = 22.29.

Therefore, the number of five-point questions (f) is approximately 22.29.