An algebra test contains 38 problems. Some of the problems are worth 2 points each. The rest of the questions are worth 3 points each. A perfect score is 100 points.How many problems are worth 2 points? How many problems are worth 3 points?
Accepted Solution
A:
Let 'x' be the problems worth 2 points.Let 'y' be the problems worth 3 points.Since, there are 38 total problems.So, [tex]x+y =38[/tex] (equation 1)x = 38-ySince, a perfect score is 100 points.So, [tex]2x+3y = 100[/tex] (equation 2)Substituting the value of 'x', we get[tex]2(38-y)+3y=100[/tex][tex]76-2y+3y=100[/tex][tex]76+y = 100[/tex]y = 24x+y = 38x = 38-24 = 14So, 14 problems are worth 2 points and 24 problems are worth 3 points.