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 189. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 15. 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.

Answer 1

87 people in the restaurant, 45 people eat in the car and 57 people eat at home.

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
`x+y+z=189`.

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
`y+z=x+15`.

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`

Substituting this value of x in the third equation we can get the value of z.

`87=z+30\\z=57`

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`

Therefore, 87 people in the restaurant, 45 people eat in the car and 57 people eat at home.