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10 December, 11:57

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.

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  1. 10 December, 12:07
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    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

    Step-by-step 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
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