Answer:
There were 240 cupcakes in the bakery
Step-by-step explanation:
Assume that the number of boxes used is x
∵ If 6 cups were placed in the box, there would be 20 boxes left
∴ The number of cups in each box = 6
∴ The number of boxes used = (x - 20)
→ Multiply the number of cups in each box by the number of boxes
used to find the total number of cups
∵ The number of cups = 6(x - 20)
∴ The number of cups = 6x - 120 ⇒ (1)
∵ If 3 cupcakes were placed in each box, it would run out of 20 boxes
∴ The number of cups in each box = 3
∴ The number of boxes used = (x + 20)
→ Multiply the number of cups in each box by the number of boxes
used to find the total number of cups
∵ The number of cups3(x + 20)
∴ The number of cups = 3x + 60 ⇒ (2)
∵ The number of cups is the same in the two cases
→ Equate the right sides of (1) and (2)
∴ 6x - 120 = 3x + 60
→ Add 120 to both sides
∴ 6x = 3x + 180
→ Subtract 3x from both sides
∴ 3x = 180
→ Divide both sides by 3 to find x
∴ x = 60
∴ The number of boxes used is 60
∵ In the bakery 4 cupcakes in one box
∵ The number of boxes is 60
∴ The number of cupcakes = 4 × 60
∴ The number of cupcakes = 240
∴ There were 240 cupcakes
