SOLUTION: You take a test in which there are 247 points possible. The test consists of true/false questions worth 2 points each, multiple choice questions worth 5 points each, and essay ques

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You take a test in which there are 247 points possible. The test consists of true/false questions worth 2 points each, multiple choice questions worth 5 points each, and essay ques      Log On


   

Question 1098810: You take a test in which there are 247 points possible. The test consists of true/false questions worth 2 points each, multiple choice questions worth 5 points each, and essay questions worth 10 points each. There are 24 more multiple choice questions than true/false questions. There are 7 times as many multiple choice questions on the exam as there are essay questions.
How many True/False Questions are there:
How many Multiple Choice Question are there:
How many Essay Questions are there:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
X-number of true false questions
Y-number of multiple choice questions
Z-number of essay questions
.
.
1.2X%2B5Y%2B10Z=247
2.Y=24%2BX
3.Y=7Z
From 2,
X=Y-24
From 3,
Z=Y%2F7
Substituting into 1,
2%28Y-24%29%2B5Y%2B10%28Y%2F7%29=247
Multiplying both sides by 7,
14%28Y-24%29%2B35Y%2B10Y=1729
14Y-336%2B45Y=1729
59Y=2065
Solve for Y then use the other equations to solve for X and Z.