The numbers are the sum of each row and column

Question

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

2 tulips two trees equal 28

two sunflowrs two trees equal 30

one tulip three leafs equal 18

three leafs and one tree equal 20

what is the value of the leaf

Answer 1

Let's assign variables to each symbol:

• Tulip = \( T \)
• Tree = \( R \)
• Sunflower = \( S \)
• Leaf = \( L \)

Now we can write down the system of equations based on the provided statements:

1. \( 2T + 2R = 28 \)
2. \( 2S + 2R = 30 \)
3. \( T + 3L = 18 \)
4. \( 3L + R = 20 \)

Let's simplify each equation:

1. From \( 2T + 2R = 28 \), we can divide by 2: \[ T + R = 14 \quad \text{(Equation 1)} \]

2. From \( 2S + 2R = 30 \), we can divide by 2: \[ S + R = 15 \quad \text{(Equation 2)} \]

3. The third equation remains: \[ T + 3L = 18 \quad \text{(Equation 3)} \]

4. The fourth equation remains: \[ 3L + R = 20 \quad \text{(Equation 4)} \]

Next, we can manipulate these equations to find the variable values.

Step 1: Solve for \( R \)

From Equation 1: \[ R = 14 - T \quad \text{(Substituted into other equations)} \]

Step 2: Substitute \( R \) into Equation 2

Substituting \( R = 14 - T \) into Equation 2: \[ S + (14 - T) = 15 \ S - T = 1 \quad \text{(Equation 5)} \]

Step 3: Substitute \( R \) into Equation 4

Substituting \( R = 14 - T \) into Equation 4: \[ 3L + (14 - T) = 20 \ 3L - T = 6 \quad \text{(Equation 6)} \]

Step 4: Solve the system of Equations 3 and 6

Now we have:

• \( T + 3L = 18 \) (Equation 3)
• \( 3L - T = 6 \) (Equation 6)

We can add these two equations together to eliminate \( T \): \[ (T + 3L) + (3L - T) = 18 + 6 \ 6L = 24 \ L = 4 \]

Step 5: Substitute \( L \) back to find \( T \) and \( R \)

Substituting \( L = 4 \) into Equation 3: \[ T + 3(4) = 18 \ T + 12 = 18 \ T = 6 \]

Now substituting \( T = 6 \) into Equation 1 to find \( R \): \[ 6 + R = 14 \ R = 8 \]

Step 6: Substitute to find \( S \)

Now substituting \( T = 6 \) into Equation 5 to find \( S \): \[ S - 6 = 1 \ S = 7 \]

Summary of Values:

• Tulip \( T = 6 \)
• Tree \( R = 8 \)
• Sunflower \( S = 7 \)
• Leaf \( L = 4 \)

Thus, the value of the leaf \( L \) is \( \boxed{4} \).