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: Emma’s Sea Glass
* Goal: Find how many days it takes to reach 60 pieces.
* Start: Emma has 16 pieces.
* Rate: She adds 2 pieces per day.
* Step 1: Find out how many *new* pieces she needs.
$60 \text{ (total)} - 16 \text{ (start)} = 44$ pieces needed.
* Step 2: Divide the needed pieces by the daily rate.
$44 / 2 = 22$ days.
* Check: $16 + (2 \times 22) = 16 + 44 = 60$. Correct.

Problem 2: Consecutive Even Numbers
* Goal: Find the smallest of three consecutive even numbers that add up to 48.
* Logic: Let the smallest number be $x$. The next even number is $x + 2$, and the one after that is $x + 4$.
* Equation: $x + (x + 2) + (x + 4) = 48$
* Step 1: Combine like terms.
$3x + 6 = 48$
* Step 2: Subtract 6 from both sides.
$3x = 42$
* Step 3: Divide by 3.
$x = 14$
* Check: The numbers are 14, 16, and 18.
$14 + 16 + 18 = 48$. Correct. The smallest is 14.

Problem 3: Philippe’s Hats
* Goal: Find how many hats he bought on Monday.
* Let $m$ be the hats bought on Monday.
* Tuesday: He bought 5 more, so Tuesday = $m + 5$.
* Total before Wednesday: Monday + Tuesday = $m + (m + 5) = 2m + 5$.
* Wednesday: Half were destroyed, leaving him with 17. This means the remaining half equals 17. So, the total before destruction was $17 \times 2 = 34$.
* Equation: Set the total equal to 34.
$2m + 5 = 34$
* Step 1: Subtract 5 from both sides.
$2m = 29$ ... Wait, let me re-read carefully.
"On Wednesday half of the total number of hats that he had was destroyed and he was left with 17 hats."
If he is left with 17, and that represents half, then the total before destruction was $17 \times 2 = 34$.
So, Total Hats (Mon + Tue) = 34.
$m + (m + 5) = 34$
$2m + 5 = 34$
$2m = 29$
$m = 14.5$

*Self-Correction/Verification:* You cannot buy half a hat in this context usually. Let me re-read the problem text in the image very closely.
"Philippe bought some hats on Monday. On Tuesday he bought 5 hats more. On Wednesday half of the total number of hats that he had was destroyed and he was left with 17 hats. How many hats did he buy on Monday?"

Let's re-calculate.
Left with 17.
Since half were destroyed, the amount before destruction was $17 \times 2 = 34$.
Total hats = Monday ($m$) + Tuesday ($m+5$).
$m + m + 5 = 34$
$2m = 29$
$m = 14.5$

Is it possible the problem implies integer answers? Usually, these worksheets do. Let me check if I misread "5 hats more". No, it says "5 hats more". Let me check "left with 17". Yes.

Let's look at Problem 5 to see if there's a pattern of non-integers? No, Problem 5 likely results in an integer.
Let me re-read Problem 3 again. Maybe "bought 5 hats more" means he bought 5 hats *total* on Tuesday? No, "5 hats more" usually implies addition to the previous amount or just adding 5 to the count. "He bought 5 hats more [than Monday]" is the standard interpretation for algebra word problems of this level.

Alternative interpretation: Maybe he bought 5 hats on Tuesday (absolute number)?
If Tuesday = 5, then Total = $m + 5$.
Half destroyed, left with 17. Total = 34.
$m + 5 = 34 \rightarrow m = 29$.

Which phrasing is more common? "On Tuesday he bought 5 hats more." vs "On Tuesday he bought 5 more hats."
Actually, looking at the grammar "bought 5 hats more", it is slightly ambiguous. However, in standard algebra problems:
Interpretation A: Tuesday = Monday + 5. Result: 14.5 hats.
Interpretation B: Tuesday = 5 hats. Result: 29 hats.

Let's look at the wording again. "On Tuesday he bought 5 hats more." This is poor phrasing for "5 more hats than Monday". It often just means he added 5 hats to his collection. If it meant "5 more than Monday", it would usually say "5 more hats *than Monday*". Without the comparison object, "bought 5 hats more" likely acts as "bought 5 additional hats".

Let's try Interpretation B (Tuesday = 5 hats):
Monday: $m$
Tuesday: 5
Total: $m + 5$
Half destroyed, 17 left $\rightarrow$ Total was 34.
$m + 5 = 34$
$m = 29$.

Let's try Interpretation A again (Tuesday = $m + 5$):
Monday: $m$
Tuesday: $m + 5$
Total: $2m + 5$
Half destroyed, 17 left $\rightarrow$ Total was 34.
$2m + 5 = 34$
$2m = 29$
$m = 14.5$.

Given that this is a school worksheet, 14.5 hats is unlikely. You don't buy half a hat. Therefore, the intended meaning of "bought 5 hats more" is almost certainly "bought 5 additional hats" (meaning Tuesday's purchase was just 5 hats).

*Revised Logic for Problem 3:*
1. He ends with 17 hats.
2. Since half were destroyed, he must have had $17 \times 2 = 34$ hats before Wednesday.
3. These 34 hats came from Monday and Tuesday.
4. Tuesday he bought "5 hats more" (interpreted as 5 additional hats to the collection).
5. So, Monday's hats + 5 = 34.
6. Monday's hats = $34 - 5 = 29$.

Problem 4: Sum of three times x and 4
* Translation: "Three times $x$" is $3x$. "Sum of... and 4" means add 4. "Is 25" means equals 25.
* Equation: $3x + 4 = 25$
* Step 1: Subtract 4 from both sides.
$3x = 21$
* Step 2: Divide by 3.
$x = 7$
* Check: $3(7) + 4 = 21 + 4 = 25$. Correct.

Problem 5: Evan’s Story Books
* Goal: Find starting number of books.
* Let $b$ be the starting number.
* Step 1: Sold half. Remaining = $b / 2$ (or $0.5b$).
* Step 2: Bought 17 more. Current = $(b / 2) + 17$.
* Result: He now has 32.
* Equation: $\frac{b}{2} + 17 = 32$
* Step 1: Subtract 17 from both sides.
$\frac{b}{2} = 15$
* Step 2: Multiply by 2 to isolate $b$.
$b = 30$
* Check: Start with 30. Sell half (15 left). Buy 17 ($15 + 17 = 32$). Correct.

Final Answer:
1. 22 days
2. 14
3. 29 hats
4. x = 7
5. 30 books