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

## If there are x correct and y incorrect, then we have

x+y=10
5x-2y = 29

Now just solve for x.

## Let's assume Nancy had x correct answers out of 10 problems.

Since each correct answer is worth 5 points, Nancy earned 5x points for the correct answers.
And since each incorrect answer deducts 2 points, Nancy would lose 2(10-x) = 20-2x points for the incorrect answers.
Given that Nancy scored 29 points in total, we can set up the equation:
5x - (20-2x) = 29
Simplifying the equation:
5x - 20 + 2x = 29
Combining like terms:
7x - 20 = 29
Adding 20 to both sides:
7x = 49
Dividing both sides by 7:
x = 7

## To find the number of correct answers Nancy had, let's set up an equation based on the given information.

Let's assume the number of correct answers Nancy had as 'x'.

Since each correct answer is worth 5 points, the total points Nancy received for the correct answers would be 5x.

And since each incorrect answer deducts 2 points, the total points Nancy lost for incorrect answers would be 2(10 - x), where (10 - x) represents the number of incorrect answers.

Given that Nancy scored 29 points in total, we can now set up the equation:

5x - 2(10 - x) = 29

First, let's simplify the equation:

5x - 20 + 2x = 29

Combining like terms:

7x - 20 = 29

Now, let's isolate the variable by adding 20 to both sides:

7x = 49

Finally, we can solve for x by dividing both sides by 7:

x = 7