sm1510 wrote:
At a restaurant, a group of friends ordered four main dishes and three side dishes at a total cost of $91. The prices of the seven items, in dollars, were all different integers, and every main dish cost more than every side dish. What was the price, in dollars, of the most expensive side dish?
(1) The most expensive main dish cost $16.
(2) The least expensive side dish cost $10.
7 dishes, all with different price.
\(M_1, M_2,M_3,M_4,S_1,S_2,S_3\) is the descending order of cost. We are looking for \(S_1\).
Such questions will invariably either have a statement giving the lowest possible price of most expensive object or otherwise. So, let us work on them.Total price is 91, so the average price is 91/7 or 13.
maximum possible lowest price.=>
13 in case there is no restriction of having different costs........13,13,13,13,13,13,13
=>
10 in case there is restriction of having different costs.....16,15,14,13,12,11 and 10 are possible prices for side dishes.
minimum possible highest price.=>
13 in case there is no restriction of having different costs...............13,13,13,13,13,13,13
=>
10 in case there is restriction of having different costs.....16,15,14,13,12,11 and 10 are possible prices for side dishes.
(1) The most expensive main dish cost $16.
Only possibility is when the prices are 16,15,14,13,12,11 and 10.
So, \(S_1=12\)
(2) The least expensive side dish cost $10
Only possibility is when the prices are 16,15,14,13,12,11 and 10.
So, \(S_1=12\)
D