A test has twenty questions worth 100 points. The test consists of x true-false questions worth 4 points each and y multiple choice questions worth 8 points each. How many of each type of question are on the test?

Answer:Number of true-false questions  =15Number of multiple choice questions  =5Step-by-step explanation:Number of true-false questions  =[tex]x[/tex]Number of multiple choice questions  =[tex]y[/tex]Total number of question =[tex]x+y=20[/tex]Points for true-false questions = 4Total points for true-false questions = [tex]4\times x =4x[/tex]Points for multiple choice questions = 8Total points for multiple choice questions = [tex]8\times y =8y[/tex]Total points of the test = [tex]4x+8y=100[/tex]We have 2 equations now:(1) [tex]x+y=20[/tex](2) [tex]4x+8y=100[/tex]We need to solve the 2 equations to find [tex]x[/tex] and [tex]y[/tex].Dividing equation 2 by 4.[tex]\frac{4x+8y}{4}=\frac{100}{4}[/tex](2a) [tex]x+2y=25[/tex]Multiplying equation (2a) with (-1) [tex]-1(x+2y)=25\times (-1)[/tex](2b) [tex]-x-2y=-25[/tex]Adding equation (2a) with equation (1).[tex]x+y=20[/tex][tex]-x-2y=-25[/tex][tex]-y=-5[/tex][tex]y=5[/tex]      [ Divided both sides by -1]Substituting value of [tex]y[/tex] in equation (1).[tex]x+5=20[/tex]Subtracting both sides by 5.[tex]x+5-5=20-5[/tex][tex]x=15[/tex]∴[tex]x=15 \ and\ y=5[/tex]Number of true-false questions  =15Number of multiple choice questions  =5