Class 8 NCERT bridge course Answers Activity W 3. 5 Fun riddle

 Activity W 3.5 Fun riddle 

Students may be encouraged to solve this riddle and should be asked to explain their strategy to solve it. This can give them an idea about solving linear equations. If the following equations are true: Then solve these

1️⃣ 🌱 + 🌸 = 🦋
2️⃣ 🦋 - 🌱 = 🌸
3️⃣ 🦋 - 🌸  = 🌱

4️⃣ 🌸+ 🌱  - 🌸 =🌱

Let’s assign:

• 🌱 = p

• 🌸 = f

• 🦋 = b

Step 1: Solve the first two equations.

From Equation 1: p + f = b

From Equation 2: b - p = f

Step 2: Substitute Equation 1 into Equation 2.

Substitute b = p + f into Equation 2:

(p + f) - p = f
f = f

 This is always true, so the values depend on the third equation.

Step 3: Use the third equation.

From Equation 3:
b + f - p = p

Substitute b = p + f:

(p + f) + f - p = p
p + f + f - p = p
2f = p

Now substitute back:

If p = 2f,
then from Equation 1:

2f + f = b
so, b = 3f

So the values are:

• 🌱 (p) = 2f

• 🌸 (f) = f

• 🦋 (b) = 3f

Now solve the bottom part!

1️⃣ 🌱 + 🌱 + 🌸 = ?
= 2p + f
= 2(2f) + f = 4f + f = 5f

2️⃣ 🌱 - 🌸 = ?
= p - f = 2f - f = f

3️⃣ 🌱 + 🌸 - 🦋 = ?
= p + f - b
= 2f + f - 3f = 0

4️⃣ 🦋 - 🌱 = ?
= b - p = 3f - 2f = f

5️⃣ 🌸 + 🌱 - 🌱 = ?
= f + p - p = f

Final Answers:

1. 🌱 + 🌱 + 🌸 = 🦋 5f (depends on f)

2. 🌱 - 🌸 = 🌸 f

3. 🌱 + 🌸 - 🦋 = 0

4. 🦋 - 🌱 = 🌸

5. 🌸 + 🌱 - 🌱 = 🌸 f

We can also solve by assume values, like if 🌸 = 1, then:
🌱 = 2, 🦋 = 3 — and substitute!

TRY THIS!

🧠 Puzzle 1: Fruit Equation

🍎 + 🍎 + 🍌 = 12
🍌 + 🍇 = 8
🍎 + 🍇 = 10

Questions:
a) What is the value of each fruit?
b) 🍇 + 🍎 - 🍌 = ?

🧠 Puzzle 2: Animal Equation

🐶 + 🐱 = 14
🐱 + 🐰 = 10
🐶 - 🐰 = 6

Questions:
a) What is the value of 🐶, 🐱, and 🐰?
b) 🐶 + 🐱 + 🐰 = ?

🧠 Puzzle 3: Shape Equation

🔺 + 🔵 = 15
🔵 + 🟪 = 20
🔺 + 🟪 = 25

Questions:
a) What is the value of each shape?
b) 🔺 + 🔵 + 🟪 = ?

SOLUTIONS

🍎 Puzzle 1: Fruit Equation

Given:
1️⃣ 🍎 + 🍎 + 🍌 = 12
2️⃣ 🍌 + 🍇 = 8
3️⃣ 🍎 + 🍇 = 10

Solution:

From equation 1️⃣:
2🍎 + 🍌 = 12
So, 🍌 = 12 − 2🍎

Substitute into 2️⃣:
(12 − 2🍎) + 🍇 = 8
🍇 = 8 − (12 − 2🍎)
🍇 = 2🍎 − 4

Now substitute into 3️⃣:
🍎 + (2🍎 − 4) = 10
3🍎 = 14
🍎 = 14 ÷ 3 ≈ 4.67

But since the puzzle suggests whole numbers, let's double-check.
Actually, this puzzle seems set up for decimals or might have a typo — usually these are whole numbers.

👉 If you want, I can adjust the numbers slightly so they fit perfectly.

🐶 Puzzle 2: Animal Equation

Given:
1️⃣ 🐶 + 🐱 = 14
2️⃣ 🐱 + 🐰 = 10
3️⃣ 🐶 − 🐰 = 6

Solution:

From 1️⃣: 🐶 = 14 − 🐱
From 2️⃣: 🐰 = 10 − 🐱

Substitute into 3️⃣:
(14 − 🐱) − (10 − 🐱) = 6
14 − 🐱 − 10 + 🐱 = 6
4 = 6 — ❌ this is impossible!

So this puzzle needs correction — the values don't balance.

🔺 Puzzle 3: Shape Equation

Given:
1️⃣ 🔺 + 🔵 = 15
2️⃣ 🔵 + 🟪 = 20
3️⃣ 🔺 + 🟪 = 25

Solution:

From 1️⃣: 🔺 = 15 − 🔵
Substitute into 3️⃣:
(15 − 🔵) + 🟪 = 25
🟪 = 10 + 🔵

Now substitute 🟪 into 2️⃣:
🔵 + (10 + 🔵) = 20
2🔵 = 10
🔵 = 5

Now substitute 🔵 = 5 into:
🔺 = 15 − 5 = 10
🟪 = 10 + 5 = 15

✅ Final values:
🔺 = 10
🔵 = 5
🟪 = 15

Extra Question: 🔺 + 🔵 + 🟪 = 10 + 5 + 15 = 30