Question

Kenny and Ben start competing businesses selling hats. Kenny buys supplies, costing $3, before he starts selling his
hats for $0.50 each.
Ben sells his hats for $0.25 each and spent only $1 on supplies. At
what point have they sold the same number of hats and made the
same profit (income minus costs)?
Write your answer as a coordinate point (hats, profit). HELP PLZ WHAT ARE THE EQUATIONS??

Answer 1

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Answer:

  (8, 1)

Step-by-step explanation:

Let x represent the number of hats sold by each seller.

__

Kenny's cost: $3

Kenny's revenue: $0.50x

Kenny's profit = revenue - cost: y = 0.50x -3

__

Ben's cost: $1

Ben's revenue: $0.25x

Ben's profit = revenue - cost: y = 0.25x -1

__

The profit and sales will be the same when the same (x, y) values satisfy both profit equations.

  y = 0.50x -3

  y = 0.25x -1

  0.50x -3 = 0.25x -1 . . . . . substitute for y

  0.25x = 2 . . . . . . . . . . . add 3-0.25x

  x = 8 . . . . . . . . . . multiply by 4

  y = 0.25x -1 = 2 -1 = 1 . . . using Ben's profit equation

The profit and sales will be the same for ...

  (hats, profit) = (8, 1)