Solve this:
1) In a division statement, the quotient is 5 and the remainder is 6. The difference between the divisor and the dividend is 38. Find the values of the dividend and the divisor.
Let the divisor be D and the dividend be X.
According to the division statement:
X = D * 5 + 6
Given that the difference between the divisor and the dividend is 38:
D - X = 38
Substitute the first equation into the second equation:
D - (D * 5 + 6) = 38
D - 5D - 6 = 38
-4D - 6 = 38
-4D = 44
D = -11
Now, substitute the value of D back into the first equation:
X = (-11) * 5 + 6
X = -55 + 6
X = -49
Therefore, the dividend is -49 and the divisor is -11.