Question

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.

Answer 1

Answer:

• 80 restaurant purchased meals are eaten in a restaurant

• 31 meals are eaten in a car

• 60 meals are eaten at home

Step-by-step explanation:

Let us suppose r be the total number of meals eaten in a restaurant

Let us suppose c be the total number of meals eaten in a car

Let us suppose h be the total number of meals eaten in a home

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

Substituting Equation [B] into [A],

$r + c + h = 171.....[A]$

$r + r + 11 = 171$

$2r + 11 = 171$

$2r = 160$

$r = 80$

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

$80 = h + 20$

$h = 60$

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

$80 + c + 60 = 171$

$c = 171 - 60 - 80$

$c = 31$

Therefore,

• 80 restaurant purchased meals are eaten in a restaurant

• 31 meals are eaten in a car

• 60 meals are eaten at home

Verification:

$r + c + h = 171$

Putting $r = 80$, $c = 31$ and $h = 60$ in $r + c + h = 171$

$80 + 31 + 60 = 171$

$171 = 171$

Keywords: number, equation

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