How many correct answers did she have?

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

Let C be the number of correct answers and I be the number of incorrect answers.

Given total problems is 10 => C+I = 10  -----(1)

Nancy scored 29 points for all 10 problems;
=> 5C-2I = 29 -------(2)

Multiplying equation (1) by 2 gives
2C+2I = 20 -----(3)

(2)+(3) gives
7C = 49
C = 7

Nancy have 7 correct answers.