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kenny6666 [7]
3 years ago
9

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Mathematics
2 answers:
wel3 years ago
6 0
X+y=24 so we can say

x=24-y making 3x+5y=100 become

3(24-y)+5y=100

72-3y+5y=100

72+2y=100

2y=28

y=14, since x=24-y

x=10

So there are 10 3-point questions and 14 5-point questions.
devlian [24]3 years ago
3 0

Answer:

The test contains 10 three-point questions and 14 five-point questions.

Step-by-step explanation:

We are given that A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points

System of equations: x+y=24  --a

                                   3x+5y=100 --b

Where x denotes x is the number of 3-point questions and y is the number of 5-point questions

Now solve equation a and b by substitution method

Substitute the value of x from a in b

⇒3(24-y)+5y=100

⇒72-3y+5y=100

⇒72+2y=100

⇒2y=28

⇒y=\frac{28}{2}

⇒y=14

Substitute the value of y in equation a to get the value of x

x+14=24

x=10

Thus 10 is the number of 3-point questions.

14  is the number of 5-point questions.

Thus Option 2 is correct.

The test contains 10 three-point questions and 14 five-point questions.

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