The total number of restaurant purchased meals that the average person will eat in a restaurant, and a car, or at home in a year is 171 . The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 11. Twenty more restaurant purchased meals will be eating 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 eating at home.

The total number of meals eaten in a restaurant, in a car or at home is given as 163. Hence, [tex]r + c + h = 171.....[A][/tex]
The total number meals eaten in a car or at home exceeds the number eaten in a restaurant by 11. Hence, [tex]c + h = r + 11.....[B][/tex]
Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Hence, [tex]r = h + 20.....[C][/tex]

Substituting Equation [B] into [A],

[tex]r + c + h = 171.....[A][/tex]

[tex]r + r + 11 = 171[/tex]

[tex]2r + 11 = 171[/tex]

[tex]2r = 160[/tex]

[tex]r = 80[/tex]

Putting [tex]r = 80[/tex] in [tex]r = h + 20.....[C][/tex]

[tex]80 = h + 20[/tex]

[tex]h = 60[/tex]

Putting [tex]r = 80[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171.....[A][/tex]

[tex]80 + c + 60 = 171[/tex]

[tex]c = 171 - 60 - 80[/tex]

[tex]c = 31[/tex]

Therefore,

Verification:

[tex]r + c + h = 171[/tex]

Putting [tex]r = 80[/tex], [tex]c = 31[/tex] and [tex]h = 60[/tex] in [tex]r + c + h = 171[/tex]

[tex]80 + 31 + 60 = 171[/tex]

[tex]171 = 171[/tex]

Keywords: number, equation

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