Question

Badia is the apprentice at the local screws and nails factory. The other day she made some six - inch nails. Charli who works next to her made one and half times as many as Badia, but Siva made twice as many as Charli. They all made a total of 110 six - inch nails.

45. How many did Badia make?
46. How many did Charli make?
47. How many did Siva make?

Answer 1

45. 20

46. 30

47. 60

Explanation:

Let :

• Badia = x
• Charli = 1 1/2x = 1.5x
• Siva = 2(1.5)x = 3x

Solving

• x + 1.5x + 3x = 110
• 5.5x = 110
• x = 20

Solution

• Badia = 20
• Charli = 30
• Siva = 60

Answer 2

Badia made 20 nails

Charli made 30 nails

Siva made 60 nails

Explanation:

Let b = number of nails Badia made

Let c = number of nails Charli made

Let s = number of nails Siva made

Given:

• Charli made one and half times as many as Badia

⇒ Equation 1: c = 1.5b

Given:

• Siva made twice as many as Charli

⇒ Equation 2: s = 2c

Given:

• They all made a total of 110 nails

⇒ Equation 3: b + c + s = 110

Substitute Equation 1 into Equation 2:

⇒ s = 2(1.5b) = 3b

Substitute s = 3b and Equation 1 into Equation 3 and solve for b:

⇒ b + c + s = 110

⇒ b + 1.5b + 3b = 110

⇒ 5.5b = 110

⇒ b = 20

Substitute found value of b into Equation 1 and solve for c:

⇒ c = 1.5b

⇒ c = 1.5(20)

⇒ c = 30

Substitute found value of c into Equation 2 and solve for s:

⇒ s = 2c

⇒ s = 2(30)

⇒ s = 60

Therefore:

• Badia made 20 nails
• Charli made 30 nails
• Siva made 60 nails