Answer:
87 people in the restaurant, 45 people eat in the car and 57 people eat at home.
Step-by-step explanation:
Let x be 'restaurant-purchased meals eaten in a restaurant', y be the 'restaurant-purchased meals eaten in a car' and z be the 'restaurant-purchased meals eaten at home'.
We can use the given information "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" to write an equation
.
We can use the information "the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 15" to write another equation
.
We can use the information "thirty more restaurant-purchased meals will be eaten in a restaurant than at home" to write the third equation as x=z+30
Now we need to solve this system of three equations to get the values of x, y and z.
We can solve for x directly from the first two equations.
![x+x+15=189\\2x=174\\x=87](https://tex.z-dn.net/?f=x%2Bx%2B15%3D189%5C%5C2x%3D174%5C%5Cx%3D87)
Substituting this value of x in the third equation we can get the value of z.
![87=z+30\\z=57](https://tex.z-dn.net/?f=87%3Dz%2B30%5C%5Cz%3D57)
Finally, we can substitute the values of x and z in the first (or second) equation to get the value of y.
![87+y+57=189\\y+144=189\\y=45](https://tex.z-dn.net/?f=87%2By%2B57%3D189%5C%5Cy%2B144%3D189%5C%5Cy%3D45)
Therefore, 87 people in the restaurant, 45 people eat in the car and 57 people eat at home.