1. **State the problem:** Find three consecutive even integers such that 50 times the smallest is 88 less than 46 times the largest. 2. **Define variables:** Let the smallest even integer be $x$. Since the integers are consecutive even numbers, the next two are $x+2$ and $x+4$. 3. **Write the equation from the problem statement:** $$50x = 46(x+4) - 88$$ This means 50 times the smallest integer equals 46 times the largest integer minus 88. 4. **Expand and simplify:** $$50x = 46x + 184 - 88$$ $$50x = 46x + 96$$ 5. **Isolate $x$:** $$50x - 46x = 96$$ $$\cancel{50}x - \cancel{46}x = 96$$ $$4x = 96$$ 6. **Solve for $x$:** $$x = \frac{96}{4}$$ $$x = 24$$ 7. **Find the three consecutive even integers:** Smallest: $24$ Second: $24 + 2 = 26$ Third: $24 + 4 = 28$ **Answer:** The three consecutive even integers are $24$, $26$, and $28$.