78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.
What is the linear equation?
A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that the total number of meals is 169.
Assume that,
a = number of meals eaten in a restaurant
b = number of meals eaten in a car
c = number of meals eaten at home
a + b + c = 169 .....(i)
Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.
Thus b + c = a + 13 .....(ii)
Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.
a = 20 + c .....(iii)
Subtract equation (ii) from (i)
a + b + c - b - c = 169 - a - 13
2a = 156
Divide both sides by 2
a = 78
Substitute a = 78 in equation (iii)
78 = 20 +c
c = 58
Putting c =58 and a =78 in equation (ii)
b + 58 = 78 + 13
b = 33
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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 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty 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.
