Question

The numbers are the sum of each row and column
(e.g., 🌷+🌳+🌳+🌷=28). Find the value of each symbol:

2 tulips 2 trees equal 28

2 sunflowrs 2 trees equal 30

1 tulip 3 leafs equal 18

3 leafs and 1 tree equal 20

what is the value of the leaf

Answer 1

To find the value of each symbol, we can set up a system of equations based on the information given.

Let's denote:
- Tulip as \( T \)
- Tree as \( R \)
- Sunflower as \( S \)
- Leaf as \( L \)

From the given information, we can write the following equations:

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

Now let’s simplify these equations:

From Equation 1:
\[
T + R = 14 \quad (1)
\]

From Equation 2:
\[
S + R = 15 \quad (2)
\]

Now we have:
1. \( T + R = 14 \)
2. \( S + R = 15 \)
3. \( T + 3L = 18 \)
4. \( 3L + R = 20 \)

From Equation (1), we can express \( R \) in terms of \( T \):
\[
R = 14 - T \quad (3)
\]

Substitute Equation (3) into Equation (2):
\[
S + (14 - T) = 15
\]
\[
S - T = 1 \quad (4)
\]
Thus, \( S = T + 1 \).

Now, let's substitute \( R \) from Equation (3) into Equation (4):
\[
3L + (14 - T) = 20
\]
\[
3L = 6 + T
\]
\[
L = 2 + \frac{T}{3} \quad (5)
\]

Now, let’s substitute \( L \) back into Equation (3):
\[
T + 3\left(2 + \frac{T}{3}\right) = 18
\]
\[
T + 6 + T = 18
\]
\[
2T + 6 = 18
\]
\[
2T = 12
\]
\[
T = 6
\]

Now, substitute \( T = 6 \) back into Equation (3):
\[
R = 14 - T = 14 - 6 = 8
\]

Using Equation (4) to find \( S \):
\[
S = T + 1 = 6 + 1 = 7
\]

Now substitute \( T = 6 \) into Equation (5) to find \( L \):
\[
L = 2 + \frac{6}{3} = 2 + 2 = 4
\]

Thus, the values we found are:
- Tulip \( T = 6 \)
- Tree \( R = 8 \)
- Sunflower \( S = 7 \)
- Leaf \( L = 4 \)

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