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vlabodo [156]
3 years ago
8

Suppose that a teacher agrees to pay a student 10​¢for every problem in this chapter that the student solves​ correctly, and fin

es the student 5​¢for every problem done incorrectly. If at the end of 30problems they do not owe each other any​ money, how many problems did the student solve​ correctly?
Mathematics
1 answer:
Andreas93 [3]3 years ago
5 0

Answer:  10

Step-by-step explanation:

Let x be the number of correct problems and y be the number of incorrect problems.

Given:  A teacher pays a student 10​¢ for every problem in this chapter that the student solves​ correctly, and fines the student 5 ¢ for every problem done incorrectly.

At the end of 30 problems they do not owe each other any​ money.

The by considering the given information we have the following equations :-

x+y=30-----(1)\\\\ 10x-5y=0------(2)

From (2), we have

5y=10x\\\\\Rightarrow\ y=2x

Put y=2x in (1)

x+2x=30\\\\\Rightarrow\ 3x=30\Rightarrow x=10

Then,  y=2(10)=20

Hence, the number of correct problems is 10 and the number of incorrect problems is 20.

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