Answer:
<em>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.</em>
Step-by-step explanation:
Suppose, the number of meals eaten in a restaurant is
, in a car is
and at home is ![z](https://tex.z-dn.net/?f=z)
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......
![x+y+z=163 .............................(1)](https://tex.z-dn.net/?f=x%2By%2Bz%3D163%20.............................%281%29)
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......
![y+z=x+13 ................................(2)](https://tex.z-dn.net/?f=y%2Bz%3Dx%2B13%20................................%282%29)
Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. So, the third equation will be......
![x= z+20..................................(3)](https://tex.z-dn.net/?f=x%3D%20z%2B20..................................%283%29)
First, <u>substituting equation (2) into equation (1)</u>, we will get........
![x+(x+13)=163\\ \\ \Rightarrow 2x+13=163\\ \\ \Rightarrow 2x=163-13=150\\ \\ \Rightarrow x=\frac{150}{2}=75](https://tex.z-dn.net/?f=x%2B%28x%2B13%29%3D163%5C%5C%20%5C%5C%20%5CRightarrow%202x%2B13%3D163%5C%5C%20%5C%5C%20%5CRightarrow%202x%3D163-13%3D150%5C%5C%20%5C%5C%20%5CRightarrow%20x%3D%5Cfrac%7B150%7D%7B2%7D%3D75)
<em>Now plugging this
into equation (3)</em>, we will get......
![75=z+20\\ \\ \Rightarrow z=75-20= 55](https://tex.z-dn.net/?f=75%3Dz%2B20%5C%5C%20%5C%5C%20%5CRightarrow%20z%3D75-20%3D%2055)
<em>Plugging
and
into equation (1)</em> .........
![75+y+55=163\\ \\ \Rightarrow y+130=163\\ \\ \Rightarrow y=163-130=33](https://tex.z-dn.net/?f=75%2By%2B55%3D163%5C%5C%20%5C%5C%20%5CRightarrow%20y%2B130%3D163%5C%5C%20%5C%5C%20%5CRightarrow%20y%3D163-130%3D33)
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.