Find two consecutive integers such that four times the larger is 94 more than three times the smaller

1. Let the two consecutive integers be \( x \) and \( x + 1 \).
2. According to the problem, four times the larger integer is 94 more than three times the smaller integer. Therefore, the expression becomes:
4(x + 1) = 3x + 94
3. Distribute and simplify:
4x + 4 = 3x + 94
4. Subtract \( 3x \) from both sides:
x + 4 = 94
5. Subtract 4 from both sides:
x = 90
6. The larger integer is:
x + 1 = 90 + 1 = 91

Answer: The larger integer is 91, so the consecutive integers are 90 and 91.