4. Forty-eight more than the second of three consecutive odd integers is the sum of the first Ang 2/3 of the third the three integers.
Let the three consecutive odd integers be x, x+2, and x+4.
Given that forty-eight more than the second integer is equal to the sum of the first and 2/3 of the third integer:
x + 2 + 48 = x + (2/3)(x+4)
Subtract x from both sides:
2 + 48 = (1 + 2/3)x + (8/3)
50 = (3/3 + 2/3)x + (8/3)
50 = (5/3)x + (8/3)
Multiply both sides by 3 to clear the fraction:
150 = 5x + 8
Subtract 8 from both sides:
142 = 5x
Divide by 5:
x = 28
So the three consecutive odd integers are 28, 30, and 32.
Therefore, forty-eight more than the second integer (30) is 78, and 2/3 of the third integer (32) is 64/3. These two values are indeed equal.