Your teacher is giving you a test worth 100 points containing 40 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test?

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Answer 1 · 2015-09-11T16:39:05

Number of 2 mark questions #=30#
Number of 4 mark questions #=10#

Let x be the number of 2 mark questions
Let y be the number of 4 mark questions

#x + y = 40# ---------------(1)
#2x+4y=100#---------------(2)

Solve equation (1) for y
#y = 40-x#

Substitute #y = 40-x# in equation (2)

#2x +4(40-x)=100#
#2x +160-4x=100#
#2x -4x=100-160#
#-2x =-60#
#x=(-60)/(-2)=30#

Substitute #x=30# in equation (1)

#30+y=40#
#y=40-30=10#
Number of 2 mark questions #=30#
Number of 4 mark questions #=10#