Answer:
The price will be the same for both companies at 60 mugs
Explanation:
The form of the linear equation is y = m x + b, where
Assume that the number of mugs is x and the total cost of them is $y
∵ The Cup Company will make them for $4 each plus a $30
set-up charge
∴ The cost per mug = $4
∴ m = 4
∴ The fixed amount = $30
∴ b = 30
∵ x is the number of mugs
∵ y is the cost of them
→ Substitute the values of m and b in the form of the equation
∴ y = 4x + 30 ⇒ (1)
∵ Mugs Are Us will make them for $4.50 each with no set-up charge
∴ The cost per mug = $4.50
∴ m = 4.5
∴ The fixed amount = 0
∴ b = 0
∵ x is the number of mugs
∵ y is the cost of them
→ Substitute the values of m and b in the form of the equation
∴ y = 4.5x + 0
∴ y= 4.5x ⇒ (2)
∵ The price be the same for both companies
→ Equate the right sides of (1) and (2)
∴ 4.5x = 4x + 30
→ Subtract 4x from both sides
∵ 4.5x - 4x = 4x - 4x + 30
∴ 0.5x = 30
→ Divide both sides by 0.5
∴ x = 60
∴ The price will be the same for both companies at 60 mugs