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stiv31 [10]
3 years ago
6

An algebra test contains 38 problems. Some of the problems are worth 2 points each. The rest of the questions are worth 3 points

each. A perfect score is 100 points.
How many problems are worth 2 points? How many problems are worth 3 points?
Mathematics
2 answers:
Naily [24]3 years ago
5 0

Let 'x' be the problems worth 2 points.

Let 'y' be the problems worth 3 points.

Since, there are 38 total problems.

So, x+y =38 (equation 1)

x = 38-y

Since, a perfect score is 100 points.

So, 2x+3y = 100 (equation 2)

Substituting the value of 'x', we get

2(38-y)+3y=100

76-2y+3y=100

76+y = 100

y = 24

x+y = 38

x = 38-24 = 14

So, 14 problems are worth 2 points and 24 problems are worth 3 points.

lapo4ka [179]3 years ago
4 0

Total questions in the test = 38

Let 2 points questions be = x

Let 3 points questions be = y

As total questions are 38, so

x+y=38

From here, we can derive x as: x=38-y  ...... (i)

As given, few questions are 2 marks each and rest 3 marks each and perfect square is 100, so we get,

2x+3y=100   .......(ii)

Put the value of y from (i) in (ii)

2(38-y)+3y=100

76-2y+3y=100

y=24

Putting y in equation (i), we get

x=38-24

x=14

Hence, 2 points questions are = 14

3 points questions are = 24

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