An ongoing promotion at a department store gives customers 20% off the portion of their bill that is over $100. ruby's total bill at the department store after the promotion has been applied is $250. if x represents the amount of money ruby would have spent on the same purchase at the department store without the promotion, which of the following equations best models the situation?

a. 0.2x + 100 = 250
b. 0.8x + 100 = 250
c. 100 + 0.2(x - 100) = 250
d. 100 + 0.8(x - 100) = 250

The correct option is:

100 + 0.8(x - 100) = 250

Step-by-step explanation:

We are given that:

We know that a department store gives 20 % off the portion of the bill that is over 100 dollars.

Total bill is 250 and x is the amount of money she would have spent without the promotion.

The cost to which the discount applies is 0.8 ( x - 100 ).

Finally the equation we get is 100 + 0.8 (x - 100) = 250.

100+0.8(x−100)=250

Step-by-step explanation:

Since x represents the amount of money Ruby would have spent on the same purchase at the department store without the promotion, and since she only receives a discount on any portion of her bill over $100, we have that x - 100 represents the cost of the purchase to which the discount applies.

Also, since the promotion gives a 20%discount to this portion, a consumer will pay 80% of the original price for this discounted merchandise. Therefore, we have that 0.8(x−100) is the price she pays for the discounted merchandise.

Adding the pre-sale $100 to the discounted purchase price gives the money that Ruby spent on the entire purchase, or $250. This results in the following equation:

100+0.8(x−100)=250

hope it helps :)

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step-by-step explanation: