Question

In a math contest of 10 problems, 5 points were given for each correct answer and 2 points were deducted for each incorrect answer. If Nancy answered all 10 problems and scored 29 points, how many correct answers did she have?

Answer 1

Nancy had 7 correct answers.

Explanation:

To solve this problem, we can set up a system of equations. Let's assign the variable c to represent the number of correct answers Nancy had and the variable i represent the number of incorrect answers she had.

We know that the total number of answers is 10 because it is given that she answered all 10 problems. This lets us set up the first equation as follows:

c + i = 10

Then, we can set up a second equation using the number of points (29 total). We know that +5 points were added for each correct response (c) and -2 points were added for each incorrect response (i). Our next equation will look like this:

5c - 2i = 29

There are many different strategies one can use to solve systems of equations. In this case, I am going to use combination. This means I am going to add the two equations together. However, first I should multiply our first equation by 2 so that the "I" variable terms cancel out. This is modeled below:

2c + 2i = 20

Now we can add the two equations:

5c + 2c +2i - 2i = 20 +29

Now we can simplify the equation by combining the like terms to get:

7c = 49

Finally, we should divide both sides of the equation by 7 in order to get the variable c by itself on the left side of the equation.

c = 7

Therefore, the correct number of responses Nancy gave was 7.

Hope this helps!