SOLUTION: an algebra 2 test contains 38 problems. Some of the problems are worth 2 points each while the rest are worth 3 points each. A perfect score is 100 points. How many problems are wo
Question 557702: an algebra 2 test contains 38 problems. Some of the problems are worth 2 points each while the rest are worth 3 points each. A perfect score is 100 points. How many problems are worth 2 points and how many problems are worth 3 points?
I tried 2x + 3x = 100 which equals 20 but 60 and 40 is 100 but not 38
Confused not sure what i am going wrong Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! Let a = no. of 2 pointers
Let b = no. of 3 pointer
:
Write an equation for each statement:
:
"an algebra 2 test contains 38 problems."
a + b = 38
:
" Some of the problems are worth 2 points each while the rest are worth 3 points each. A perfect score is 100 points."
2a + 3b = 100
:
Multiply the 1st equation time -2, add to the above equation
-2a - 2b = -76
+2a + 3b = 100
-------------------adding eliminates a, find b
b = 24 ea 3 pointer
then obviously
38 - 24 = 14 ea 2 pointers
;
:
Check this in the 2nd statement
2(14) + 3(24) =
28 + 72 = 100
