An exam worth 145 points contains 50 questions

Question

An exam worth 145 points contains 50 questions. Some of the questions are worth two points and some are worth five points. How many two point questions are on the test? How many five point questions are on the test?

Answer 1

Answer: 35 2-point questions, and 15 5-point questions

 

Assume x 2-points question, so 50-x 5-points question

Total no of points: 2*x+5*(50-x)=145 points

2x+250-5x=145

-3x=-105

x=-105/-3=35 2-points questions

Remaining 50-35=15 5-points questions

 

 

Answer 2

Let t = two-point questions and f = five-point questions

Here's what we know:

t + f = 50 (there are a total of 50 total questions)

2t + 5f = 145 (the total points equals 145)

 

Let's solve via elimination. Multiply the first equation by -2:

-2t - 2f = -100

2t + 5f = 145

-------------------

3f = 45

Divide by 3:

f = 15

 

t + 15 = 50

t = 35

 

check:

2 * 35 + 5 * 15 = 145

70 + 75 = 145

145 = 145