Answer:
Adult=58
Step-by-step explanation:
c=child, a=adult
6.4c+9.7a=1145 equation 1
c+a=149 equation 2
a=149-c modified equation 2 to isolate a
6.4c+9.7(149-c)=1145 substitute value of a from equation 1 into equation 2
6.4c+1445.3-9.7c=1145
-3.3c=-300.3
c=91
solve for a
c+a=149
91+a=149
a=58
Check answer:
6.4c+9.7a=1145
6.4(91)+9.7(58)=1145
582.40+562.60=1145
1145=1145
Neptune's distance from the sun is d₁ = 4.503 x 10⁹ km.
Mercury's distance from the sun is d₂ = 5.791 x 10⁷ km.
Calculate the number of times d₁ is greater than d₂.
![\frac{d_{1}}{d_{2}} = \frac{4.503 \times 10^{9}}{5.791 \times 10^{7}} = 77.75859](https://tex.z-dn.net/?f=%20%5Cfrac%7Bd_%7B1%7D%7D%7Bd_%7B2%7D%7D%20%3D%20%5Cfrac%7B4.503%20%5Ctimes%2010%5E%7B9%7D%7D%7B5.791%20%5Ctimes%2010%5E%7B7%7D%7D%20%3D%2077.75859)
Answer: 7.7759 x 10⁻¹ times
Let us denote the smaller even integer by
![N](https://tex.z-dn.net/?f=N)
.
Then, the next even integer must be
![N+2](https://tex.z-dn.net/?f=N%2B2)
.
To verify, set
![N](https://tex.z-dn.net/?f=N)
as any even number, say
![174](https://tex.z-dn.net/?f=174)
.
Then, the next even integer must be 2 more than this number, i.e.
![174+2=176](https://tex.z-dn.net/?f=174%2B2%3D176)
.
The sum of these two consecutive even integers can be expressed as:
![N+(N+2)=2N+2](https://tex.z-dn.net/?f=N%2B%28N%2B2%29%3D2N%2B2)
We are told that this sum divided by four is 189.5, i.e.
![(2N+2)\div4=189.5](https://tex.z-dn.net/?f=%282N%2B2%29%5Cdiv4%3D189.5)
Multiplying both sides by 4 will reverse the division:
![(2N+2)\times1=758](https://tex.z-dn.net/?f=%282N%2B2%29%5Ctimes1%3D758)
Subtracting 2 from each side will reverse the addition:
![2N=756](https://tex.z-dn.net/?f=2N%3D756)
Dividing both sides by 2 will reverse the multiplication:
![N=378](https://tex.z-dn.net/?f=N%3D378)
Therefore, the two consecutive integers must be
378 and
380.
Check this: