Manuela is having mugs made for a fundraiser. The Cup Company will make them for $4 each plus a $30 set-up charge. Mugs Are Us will make them for $4.50 each with no set-up charge. At what amount of mugs will the price be the same for both companies?

The price will be the same for both companies at 60 mugs

Step-by-step 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

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step-by-step explanation:

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