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Tema [17]
2 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]2 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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10. 10. If AB bisects CAF, and m&lt;EAF = 72°,<br>then the m&lt;BAF =​
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The measure of ∠BAF is 54°.

Solution:

DF and CE are intersecting lines.

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∠EAF and ∠DAC are vertically opposite angles.

Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

∠DAC ≅ ∠EAF

m∠DAC = 72°

<em>Sum of the adjacent angles in a straight line = 180°</em>

m∠DAE + m∠EAF = 180°

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Subtract 72° from both sides.

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∠CAF and ∠DAE are vertically opposite angles.

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AB bisects ∠CAF means ∠CAB = ∠BAF

m∠CAB + m∠BAF = 108°

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Divide by 2 on both sides, we get

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3 years ago
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Answer:

Step-by-step explanation:

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AC= 15 + 19 = 34

8 0
3 years ago
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