SOLUTION: Your teacher is giving you a test worth 100 points containing 40 questions.There are two-point and four-point questions on the test.How many of each type of question are on the tes

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Question 119468This question is from textbook Algebra I
: Your teacher is giving you a test worth 100 points containing 40 questions.There are two-point and four-point questions on the test.How many of each type of question are on the test? This question is from textbook Algebra I

Found 2 solutions by josmiceli, Fombitz:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
What if all the questions were 4-point? then the total
score would be 4%2A40+=+160, but the total score
should be 100
What if all the questions were 2-point? Then the total
score would be 2%2A40+=+80 That's too low.
So there has to be a mixture of 2-point and 4-point.
It looks like there are more 2-point than 4-point,
because 2%2A40+=+80 is almost there.
Lets chart some numbers
2%2A40+=+80
2%2A38+=+76 and 2%2A4+=+8 the sum is 76+%2B+8+=+84
2%2A36+=+72 and 4%2A4+=+16 the sum is 72+%2B+16+=+88
2%2A34+=+68 and 6%2A4+=+24 the sum is 68+%2B+24+=+92
2%2A32+=+64 and 8%2A4+=+32 the sum is 64+%2B+32+=+96
2%2A30+=+60 and 10%2A4+=+40 the sum is 60+%2B+40+=+100
That's the answer
There are 30 2-point questions giving 60 points
and ther are 10 4-point questions giving 40 points for
a total of 100 points on a 40 question test

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let T=number of 2 point questions
Let F=number of 4 point questions
1.T%2BF=40 Total number of questions is 40.
2.2T%2B4F=100 Total point value is 100.
From 1,
T%2BF=40
T=40-F
Substitute that value into 2.
2T%2B4F=100
2%2840-F%29%2B4F=100
80-2F%2B4F=100
80%2B2F=100
2F=20
F=10
From 1,
T=40-F
T=40-10
T=30
There are 30 2 point questions and 10 4 point questions.