SOLUTION: My problem was about Solving Systems Using Substitution and this was the question "A math test is worth 100 points and has 30 problems. Each problem is worth either 3 points or 4 p

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: My problem was about Solving Systems Using Substitution and this was the question "A math test is worth 100 points and has 30 problems. Each problem is worth either 3 points or 4 p      Log On


   

Question 190224: My problem was about Solving Systems Using Substitution and this was the question "A math test is worth 100 points and has 30 problems. Each problem is worth either 3 points or 4 points. How many 4 point problems are there?" I have tried many different ways and have not been able to get an answer.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the number of 4-point problems, then (30-x) is the number of 3-point problems.
The total number of points (100) is given by 4x+3(30-x), so...
4x+3(30-x) = 100 Simplify and solve for x.
4x+90-3x = 100 Subtract 90 from both sides.
4x-3x = 10
x = 10
The number of 4-point problems is 10.
The number of 3-point problems is 30-10 = 20.
Check:
4(10)+3(20) = 40+60 = 100 This is the total number of points.
10+20 = 30 This is the total number of problems.