Question

Jim’s family is choosing whether to go to a restaurant for lunch or for dinner. The cost of a salad is $7 at lunch and $9 at dinner. The cost of a steak is $10 at lunch and $12 at dinner. Each person will choose either a salad or a steak regardless of the mealtime. Jim calculates the food bill to be $41 if they go during lunch and $51 if they go during dinner. How many people will choose a salad?
2
3
4
5

Answer 1

Let S be number choosing salad and T choosing steak. From the prices:
Lunch: 7S + 10T = 41
Dinner: 9S + 12T = 51

Subtracting: 2S + 2T = 10 → S + T = 5. Then
7S + 10(5 − S) = 41 → 7S + 50 − 10S = 41 → S = 3.

Answer: 3.