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Tema [17]
3 years ago
14

The total number of? restaurant-purchased meals that the average person will eat in a? restaurant, in a? car, or at home in a ye

ar is 163. 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.
Mathematics
1 answer:
zmey [24]3 years ago
8 0

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 x , in a car is y and at home is 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)

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)

Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. So, the third equation will be......

x= z+20..................................(3)

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

<em>Now plugging this x=75 into equation (3)</em>, we will get......

75=z+20\\ \\ \Rightarrow z=75-20= 55

<em>Plugging x=75 and z=55 into equation (1)</em> .........

75+y+55=163\\ \\ \Rightarrow y+130=163\\ \\ \Rightarrow y=163-130=33

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.

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