SOLUTION: Your science test is worth 100 points and contains 38 questions.There are two-point and five-point questions on the test.How many of each type of question are on the test?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Your science test is worth 100 points and contains 38 questions.There are two-point and five-point questions on the test.How many of each type of question are on the test?      Log On


   

Question 579126: Your science test is worth 100 points and contains 38 questions.There are two-point and five-point questions on the test.How many of each type of question are on the test?
Found 2 solutions by josmiceli, dfrazzetto:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of 2-point questions
Let +b+ = number of 5-point questions
given:
(1) +a+%2B+b+=+38+
(2) +2a+%2B+5b+=+100+
-----------------
Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) +2a+%2B+5b+=+100+
(1) +-2a+-+2b+=+-76+
+3b+=+24+
+b+=+8+
and, since
(1) +a+%2B+8+=+38+
(1) +a+=+30+
There are 30 of the 2-point questions
There are 8 of the 5-point questions
check:
(2) +2%2A30+%2B+5%2A8+=+100+
(2) +60+%2B+40+=+100+
(2) +100+=+100+
OK

Answer by dfrazzetto(283) About Me  (Show Source):
You can put this solution on YOUR website!
x+y = 38
2x+5y = 100


Solve via system of 2 equations:


Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+1%5Cy+=+38%2C%0D%0A++++2%5Cx+%2B+5%5Cy+=+100+%29%0D%0A++

Any system of equations:


has solution

or



(x=30, y=8}



30 2-point questions, and 8 5-pointers



CHECK
30+8= 38 √


30(2) + 8(5) = 60 + 40 = 100 √