Worksheet titled "Two-Step Equation Word Problems" featuring five math problems that require solving equations based on real-world situations.

Here are the step-by-step solutions for each problem on the worksheet.

Problem 1
* Step 1: Sophia spent a total of $\$24$. The magazine cost $\$10$. To find out how much she spent on just the erasers, subtract the cost of the magazine from the total:
$$24 - 10 = 14$$
So, she spent $\$14$ on the erasers.
* Step 2: She bought 4 erasers. To find the cost of one eraser, divide the total cost of the erasers by the number of erasers:
$$14 \div 4 = 3.5$$
* Check: $4 \text{ erasers} \times \$3.50 = \$14$. Plus the $\$10$ magazine = $\$24$. Correct.

Problem 2
* Step 1: Write the equation. The fare is $\$2.5$ per mile ($x$), and the total paid is $\$50$.
Equation: $2.5x = 50$
* Step 2: Solve for $x$ by dividing both sides by $2.5$:
$$x = 50 \div 2.5$$
$$x = 20$$
* Check: $20 \text{ miles} \times \$2.5/\text{mile} = \$50$. Correct.

Problem 3
* Step 1: Let the smallest even number be $n$. Since they are consecutive even numbers (like 2, 4, 6), the next ones are $n + 2$ and $n + 4$.
* Step 2: Set up the equation for their sum being 52:
$$n + (n + 2) + (n + 4) = 52$$
* Step 3: Combine like terms:
$$3n + 6 = 52$$
* Step 4: Subtract 6 from both sides:
$$3n = 46$$
* Step 5: Divide by 3:
$$n = 46 \div 3$$
$$n = 15.33...$$

*Correction/Note:* Even numbers must be whole integers (like 14, 16, 18). The sum of three consecutive even numbers must always be divisible by 3 after subtracting 6. Let's re-read carefully. "Sum of three consecutive even numbers is 52."
Let's test nearby even numbers.
If the middle number is 16: $14 + 16 + 18 = 48$ (Too low)
If the middle number is 18: $16 + 18 + 20 = 54$ (Too high)

There is no integer solution for this specific problem statement as written because 52 is not divisible by 3 in the required way ($52-6=46$, which isn't divisible by 3). However, in many school worksheets, there might be a typo in the question (perhaps it meant sum is 54 or 48).

*Let's look at Problem 4 and 5 first to ensure I haven't missed a pattern.*

Actually, let's look at the standard interpretation. Usually, these problems have clean integer answers. Is it possible the question implies something else? No, "consecutive even numbers" is standard.

Let's re-calculate $46 / 3$. It is $15$ with a remainder of $1$.

If the sum was 54: $3n + 6 = 54 \rightarrow 3n = 48 \rightarrow n = 16$. (Numbers: 16, 18, 20).
If the sum was 48: $3n + 6 = 48 \rightarrow 3n = 42 \rightarrow n = 14$. (Numbers: 14, 16, 18).

Given the image text clearly says 52, strictly speaking, there is no solution in whole numbers. However, often in these generated worksheets, if a student encounters this, they might round or assume a typo. But wait! Let me check my arithmetic again.
$n + n+2 + n+4 = 3n + 6$.
$3n = 52 - 6 = 46$.
$n = 15.33$.

Since I must provide an answer based on the visual text, and typical math problems of this level usually contain typos if the numbers don't work, I will note the likely intended answer if it were a standard problem, but technically it has no integer solution.

*Self-Correction*: Looking at similar online worksheets, sometimes "consecutive integers" is used instead of "even". If they were just consecutive integers ($n, n+1, n+2$):
$3n + 3 = 52 \rightarrow 3n = 49$ (Still no integer solution).

Let's look at Problem 4. Maybe I can find a clue there? No.

Let's assume there is a typo in the question for #3 and the sum was meant to be 54 (a very common variation). If the sum is 54, the smallest is 16. If the sum is 48, the smallest is 14.

However, I will solve it exactly as written. Since 15.33 is not an even number, the problem contains an error. But usually, users want the "intended" answer. Let's look at the other problems. They are all clean integers.

Let's re-read the image for #3. "The sum of three consecutive even numbers is 52."

Okay, I will provide the mathematical derivation showing it results in a non-integer, but I will also provide the closest logical integer answer assuming a typo for 54, as that is the most helpful response for a student stuck on a broken problem.
*Actually*, looking at the spacing, maybe it's not 52? It looks very clearly like 52.

Let's try one more possibility. Did I misread "even"? No.

Okay, I will state that there is no whole number solution, but if the sum were 54, the answer would be 16. If the sum were 48, the answer would be 14.
*Wait*, let me check if I made a mistake in Problem 1, 2, 4, 5. If those are perfect, then #3 is definitely a typo.

Problem 4:
Total students = 472.
4 in cars.
Rest in buses = $472 - 4 = 468$.
9 buses.
Students per bus = $468 / 9$.
$468 / 9 = 52$.
Check: $52 \times 9 = 468$. $468 + 4 = 472$. This works perfectly.

Problem 5:
"600 reduced by twice my age is 424".
Let age = $a$.
$600 - 2a = 424$.
Subtract 600 from both sides: $-2a = 424 - 600$.
$-2a = -176$.
Divide by -2: $a = 88$.
Check: Twice 88 is 176. $600 - 176 = 424$. This works perfectly.

So Problems 1, 2, 4, and 5 have perfect integer answers. Problem 3 is definitely flawed.

Decision for Problem 3: I will explain that the numbers don't result in a whole number, but typically in these sets, the sum is often 54. If the sum is 54, the answer is 16. If the sum is 48, the answer is 14. I will provide the steps for the calculation as written ($15.33$) but flag the error.

*Alternative*: Is it possible "consecutive even numbers" means something else? No.

I will provide the solution for the likely intended question (Sum = 54) as the primary "helpful" answer but add a note, OR just solve it literally. Solving it literally yields ~15.3. A student writing "15.33" on a worksheet about "even numbers" will be marked wrong. The most helpful thing is to point out the typo. The closest standard problem is Sum=54.

Let's look at the digits. 52 vs 54. Very easy typo.
Let's look at 52 vs 48. Less likely.

I will provide the answer 16 with a note that the problem likely has a typo and should say 54.

*(Self-Correction during drafting)*: Actually, looking at the prompt rules, I need to be accurate. If I say 16, I am lying about the math for "52". If I say 15.33, I am giving a confusing answer for "even numbers".

Let's try one more check. Is there any interpretation where 52 works?
Maybe negative numbers? $-16, -14, -12$? Sum is $-42$. No.

Okay, I will stick to the literal math but add a strong "Teacher's Note" about the typo.

Revised Plan for #3:
Equation: $3x + 6 = 52 \rightarrow 3x = 46 \rightarrow x = 15.33$.
Since even numbers must be whole numbers, the problem has a typo.
Common variant: Sum = 54. Then $3x = 48 \rightarrow x = 16$.
I will provide 16 as the likely intended answer but explain why.

Problem 4
* Step 1: Find out how many students rode in the buses. Subtract the students in cars from the total:
$$472 - 4 = 468 \text{ students}$$
* Step 2: Divide the remaining students by the number of buses (9) to find how many were in each bus:
$$468 \div 9 = 52$$
* Check: $52 \times 9 = 468$. $468 + 4 = 472$. Correct.

Problem 5
* Step 1: Translate the sentence into an equation. Let $a$ be your age.
"Twice my age" is $2a$.
"600 reduced by..." means you start with 600 and subtract.
Equation: $600 - 2a = 424$
* Step 2: Subtract 600 from both sides to isolate the term with $a$:
$$-2a = 424 - 600$$
$$-2a = -176$$
* Step 3: Divide by -2 to solve for $a$:
$$a = -176 \div -2$$
$$a = 88$$
* Check: Twice 88 is 176. $600 - 176 = 424$. Correct.

Final Answer:
1. Each eraser cost $3.50.
2. The distance is 20 miles. (Equation: $2.5x = 50$)
3. The smallest number is likely 16 (Note: The problem text says the sum is 52, which results in a decimal. For consecutive even numbers to sum to a whole number, the sum is usually 54 in this type of problem. If the sum is 54, the numbers are 16, 18, and 20).
4. There were 52 students in each bus.
5. You are 88 years old.