Question

Jester's Deli sells 640 sandwiches at a price of $8 each. A market survey shows that for every $0.10 reduction in price, 40 more sandwiches will be sold.

Let x represent the number of $0.10 reductions.

Use the Maximum Revenue information above to answer this question.
Since price cannot be negative, we have x ≤ ____________

Answer 1

The number of $0.10 reductions, represented by x, represents the number of times the price of a sandwich is reduced by $0.10. For every $0.10 reduction in price, 40 more sandwiches will be sold. Therefore, the total number of sandwiches sold is 640 + 40x. Since the price cannot be negative, x must be less than or equal to the number of times the price is reduced. In this case, the maximum number of $0.10 reductions is 80 (800 cents / 10 cents = 80 reductions). Therefore, x ≤ 80.

Step-by-step explanation:

The number of $0.10 reductions, represented by x, represents the number of times the price of a sandwich is reduced by $0.10. We know that for every $0.10 reduction in price, 40 more sandwiches will be sold. So, the number of additional sandwiches sold is 40x. Therefore, the total number of sandwiches sold is 640 + 40x. Since the price cannot be negative, x must be less than or equal to the number of times the price is reduced.

In this case, since the price is reduced by $0.10 for each reduction and the original price is $8, the maximum number of $0.10 reductions is 80 (800 cents / 10 cents = 80 reductions). Therefore, x ≤ 80.