Christmas-themed math puzzle worksheet where students solve for the value of each picture using given row totals.

Let’s solve this step by step.

We have four pictures:
- A weasel (with Santa hat)
- A Christmas tree
- A snowman
- A snowflake

Each picture is worth a different multiple of one-half, greater than 0 but less than 4. That means possible values are:
0.5, 1, 1.5, 2, 2.5, 3, 3.5

But since there are only 4 pictures, and they must all be *different*, we’ll pick 4 distinct values from that list.

Now look at the rows:

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Row 1: Snowflake + Snowman + Tree + Snowflake = 10
→ So: 2 × Snowflake + Snowman + Tree = 10

Row 2: Weasel + Tree + Weasel + Tree = 7
→ So: 2 × Weasel + 2 × Tree = 7
Divide both sides by 2:
→ Weasel + Tree = 3.5

Row 3: Snowman + Snowman + Weasel + Snowman = 12.5
→ So: 3 × Snowman + Weasel = 12.5

Row 4: Tree + Snowflake + Tree + Snowman = 9
→ So: 2 × Tree + Snowflake + Snowman = 9

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Let’s use Row 2 first because it’s simple:

From Row 2:
Weasel + Tree = 3.5 → Let’s call this Equation (A)

From Row 3:
3 × Snowman + Weasel = 12.5 → Equation (B)

Subtract Equation (A) from Equation (B):

(3 × Snowman + Weasel) - (Weasel + Tree) = 12.5 - 3.5
→ 3 × Snowman - Tree = 9 → Equation (C)

Now let’s look at Row 1:
2 × Snowflake + Snowman + Tree = 10 → Equation (D)

And Row 4:
2 × Tree + Snowflake + Snowman = 9 → Equation (E)

Let’s subtract Equation (E) from Equation (D):

(2×Snowflake + Snowman + Tree) - (2×Tree + Snowflake + Snowman) = 10 - 9
→ (2×Snowflake - Snowflake) + (Snowman - Snowman) + (Tree - 2×Tree) = 1
→ Snowflake - Tree = 1
→ Snowflake = Tree + 1 → Equation (F)

Now plug Equation (F) into Equation (E):

Equation (E): 2×Tree + Snowflake + Snowman = 9
Replace Snowflake with (Tree + 1):
→ 2×Tree + (Tree + 1) + Snowman = 9
→ 3×Tree + 1 + Snowman = 9
→ 3×Tree + Snowman = 8 → Equation (G)

Now recall Equation (C):
3 × Snowman - Tree = 9

So now we have two equations:

(G) 3×Tree + Snowman = 8
(C) 3×Snowman - Tree = 9

Let’s solve these together.

From (G): Snowman = 8 - 3×Tree

Plug into (C):

3×(8 - 3×Tree) - Tree = 9
→ 24 - 9×Tree - Tree = 9
→ 24 - 10×Tree = 9
→ -10×Tree = 9 - 24 = -15
→ Tree = (-15)/(-10) = 1.5

Now find others:

Tree = 1.5

From Equation (A): Weasel + Tree = 3.5 → Weasel = 3.5 - 1.5 = 2

From Equation (F): Snowflake = Tree + 1 = 1.5 + 1 = 2.5

From Equation (G): 3×Tree + Snowman = 8 → 3×1.5 + Snowman = 8 → 4.5 + Snowman = 8 → Snowman = 3.5

Check if all values are different multiples of 0.5 between 0 and 4:

- Weasel = 2 ✔
- Tree = 1.5 ✔
- Snowman = 3.5 ✔
- Snowflake = 2.5 ✔

All different, all valid.

Now verify with original rows:

Row 1: Snowflake + Snowman + Tree + Snowflake = 2.5 + 3.5 + 1.5 + 2.5 = 10 ✔
Row 2: Weasel + Tree + Weasel + Tree = 2 + 1.5 + 2 + 1.5 = 7 ✔
Row 3: Snowman + Snowman + Weasel + Snowman = 3.5 + 3.5 + 2 + 3.5 = 12.5 ✔
Row 4: Tree + Snowflake + Tree + Snowman = 1.5 + 2.5 + 1.5 + 3.5 = 9 ✔

Perfect!

Final Answer:
Weasel = 2
Tree = 1.5
Snowman = 3.5
Snowflake = 2.5