Luke buys a certain brand of cereal that costs $10 per box. Luke changes to a super-saving brand of the same size. The equation shows the price, y, as a function of the number of boxes, x, for the new brand.
Part A: How many more dollars is the price of a box of Luke's original brand of cereal than the price of a box of the super-saving brand? Show your work.
Part B: How much money does Luke save each month with the change in cereal brand if he buys 5 cereal boxes each month? Show your work. (10 points)
Part A:
The price of a box of Luke's original brand is $10.
The price of a box of the super-saving brand is given by the equation y = 5x.
To find how many more dollars the price of a box of Luke's original brand is than the price of a box of the super-saving brand, we need to subtract the cost of the super-saving brand from the cost of the original brand.
So, the difference in price is $10 - ($5 * x) = $10 - $5x.
Part B:
If Luke buys 5 cereal boxes each month, we can substitute x = 5 into the equation for the difference in price to find how much money Luke saves each month.
The difference in price is $10 - ($5 * 5) = $10 - $25 = -$15.
Since the result is negative, Luke is not saving money but spending an additional $15 each month compared to buying the original brand of cereal.