The numbers are the sum of each row and column.

Question

(e.g., flower + tree + tree + flower = 28.) Find the value of each symbol:

Flower:
Tree:
Sunflower:
Leaf:
?
COLUMN:
Flower + tree + tree + flower = 28
Sunflower + tree + sunflower + tree = 30
Leaf + flower + leaf + leaf = 18
Leaf + tree + leaf + leaf = 20.

ROW:
Flower + sunflower + leaf + leaf = ?
tree + flower + tree + tree = 30
Leaf + leaf + sunflower + tree = 23
Leaf + leaf + tree + flower = 22

Answer 1

Let's denote:

• Flower = F
• Tree = T
• Sunflower = S
• Leaf = L

We have the following equations based on the column and row sums provided:

From the Columns:

1. \( 2F + 2T = 28 \) (From the first column)
2. \( 2S + 2T = 30 \) (From the second column)
3. \( 3L + F = 18 \) (From the third column)
4. \( 3L + T = 20 \) (From the fourth column)

From the Rows: 5. \( F + S + 2L = ? \) (From the first row) 6. \( T + 2F + 2T = 30 \) (From the second row) 7. \( 2L + S + T = 23 \) (From the third row) 8. \( 2L + F + T = 22 \) (From the fourth row)

Now let's solve these equations:

From the first column equation: \[ 2F + 2T = 28 \implies F + T = 14 \quad \text{(dividing by 2)} \quad \text{(Equation 1)} \]

From the second column equation: \[ 2S + 2T = 30 \implies S + T = 15 \quad \text{(dividing by 2)} \quad \text{(Equation 2)} \]

From the third column equation: \[ 3L + F = 18 \quad \text{(Equation 3)} \]

From the fourth column equation: \[ 3L + T = 20 \quad \text{(Equation 4)} \]

Now let's express F and T from Equations 1 and 2: From Equation 1: \[ F = 14 - T \quad \text{(Substituting in Equation 3)} \]

Substituting \( F \) in Equation 3: \[ 3L + (14 - T) = 18 \] \[ 3L - T = 4 \quad \text{(Equation 5)} \]

Now substituting \( T \) in Equation 4 as well: From Equation 2: \[ T = 15 - S \quad \text{(Substituting in Equation 4)} \]

Substituting \( T \) in Equation 4: \[ 3L + (15 - S) = 20 \] \[ 3L - S = 5 \quad \text{(Equation 6)} \]

Now we have: Equation 5: \[ 3L - T = 4 \] Equation 6: \[ 3L - S = 5 \]

Now let's subtract Equation 5 from Equation 6: \[ (3L - S) - (3L - T) = 5 - 4 \] \[ T - S = 1 \] \[ T = S + 1 \quad \text{(Equation 7)} \]

Now substitute Equation 7 back into Equation 2: \[ S + (S + 1) = 15 \] \[ 2S + 1 = 15 \] \[ 2S = 14 \] \[ S = 7 \]

Using \( S \) in Equation 7: \[ T = 7 + 1 = 8 \]

Using \( T \) in Equation 1: \[ F + 8 = 14 \] \[ F = 6 \]

Now we can find \( L \) using either Equation 3 or 4. Using Equation 3: \[ 3L + 6 = 18 \] \[ 3L = 12 \] \[ L = 4 \]

Now, we have:

• Flower (F) = 6
• Tree (T) = 8
• Sunflower (S) = 7
• Leaf (L) = 4

Finally, find the value of the first row: \[ F + S + 2L = 6 + 7 + 2(4) = 6 + 7 + 8 = 21 \]

So the answers are:

• Flower: \( 6 \)
• Tree: \( 8 \)
• Sunflower: \( 7 \)
• Leaf: \( 4 \)
• Row sum: \( 21 \)