Respuesta :
Answer:
The number of restaurant-purchased meals eaten in a restaurant is 75, the number eaten in a car is 33 and the number eaten at home is 55.
Step-by-step explanation:
Suppose, the number of meals eaten in a restaurant is [tex]x[/tex] , in a car is [tex]y[/tex] and at home is [tex]z[/tex]
The total number of meals eaten in a restaurant, in a car or at home is given as 163. So, the first equation will be......
[tex]x+y+z=163 .............................(1)[/tex]
The total number meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. So, the second equation will be......
[tex]y+z=x+13 ................................(2)[/tex]
Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. So, the third equation will be......
[tex]x= z+20..................................(3)[/tex]
First, substituting equation (2) into equation (1), we will get........
[tex]x+(x+13)=163\\ \\ \Rightarrow 2x+13=163\\ \\ \Rightarrow 2x=163-13=150\\ \\ \Rightarrow x=\frac{150}{2}=75[/tex]
Now plugging this [tex]x=75[/tex] into equation (3), we will get......
[tex]75=z+20\\ \\ \Rightarrow z=75-20= 55[/tex]
Plugging [tex]x=75[/tex] and [tex]z=55[/tex] into equation (1) .........
[tex]75+y+55=163\\ \\ \Rightarrow y+130=163\\ \\ \Rightarrow y=163-130=33[/tex]
So, the number of restaurant-purchased meals eaten in a restaurant is 75, the number eaten in a car is 33 and the number eaten at home is 55.
