Question

The total number of​ restaurant-purchased meals that the average person will eat in a​ restaurant, in a​ car, or at home in a year is 189189. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 1313. Thirty Thirty more​ restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of​ restaurant-purchased meals eaten in a​ restaurant, the number eaten in a​ car, and the number eaten at home.

Answer 1

• The number of meals eaten in a restaurant, r =88
• The number of meals eaten in the car, c=43
• The number of meals eaten at home, h=58

Explanation:

• Let the number of meals eaten in a restaurant =r
• Let the number of meals eaten in the car =c
• Let the number of meals eaten at home =h

We now interpret each statement mathematically:

The total number of​ restaurant-purchased meals that the average person will eat in a​ restaurant, in a​ car, or at home in a year is 189

• c+h+r=189

The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13

• c+h=r+13

Thirty more​ restaurant-purchased meals will be eaten in a restaurant than at home.

• r=h+30

We then solve the three derived equations simultaneously.

c+h+r=189

c+h=r+13

r=h+30

Substitute r=h+30 into c+h=r+13

c+h=r+13

c+h=h+30+13

c=43

Substitute r=h+30 and c=43 into c+h+r=189

43+h+h+30=189

2h=189-43-30

2h=116

h=58

Recall: r=h+30

r=58+30=88

Therefore: c=43, h=58, r=88

• The number of meals eaten in a restaurant, r =88
• The number of meals eaten in the car, c=43
• The number of meals eaten at home, h=58