a test that will have 30 questions and will total 100 points. The True-False questions will be 4 pts each and the Multiple-Choice questions will be 3 points each. How many of each type of question?

Question

i need help with this problem its on solving systems

Answer 1

Let's call the T/F questions variable t, and the multiple choice questions variable m. There are 30 total questions, so t + m = 30, The total points on the test is 100, and since the T/F questions are worth 4 points each, the total you can get from those is 4t. Similarly, the total points you can get from multiple choice is 3m. Put these together and 4t + 3m = 100.

Now, solve one variable in terms of the other using the first equation

t + m = 30, subtract t from both sides and m = 30 - t.

Substitute 30 - t for the m term of the second equation

4t + 3(30-t) = 100, distribute the 3.

4t + 90 - 3t = 100, simplify by combining the t terms

t + 90 = 100, solve for t

t = 10

Now plug 10 in for t in the first equation, t + m = 30, so 10 + m = 30, and so m = 20

so there are 10 T/F questions and 20 multiple choice questions

Hope this helps

Answer 2

4x+3y=100

x+y=30

x=10

y=20