The correct selling price is about $20, and the likely mistake was the manager multiplied the $12 by .67 (the 67%), got about 8, and took that as the price instead of adding it to the original 12, which is what they were supposed to do.
Here is a picture of my work. The range is solved when you subtract the biggest number from the smallest number. Hope this helps
Answer:
---- Hao Sheng
--- His father
---- His grandfather
Step-by-step explanation:
Given
![x \to Hao\ Sheng](https://tex.z-dn.net/?f=x%20%5Cto%20Hao%5C%20Sheng)
![y \to his\ father](https://tex.z-dn.net/?f=y%20%5Cto%20his%5C%20father)
![z \to his\ grandfather](https://tex.z-dn.net/?f=z%20%5Cto%20his%5C%20grandfather)
From the question, we have:
--- The average of their age
![\frac{z}{2} + \frac{y}{3} +\frac{x}{4}= 65](https://tex.z-dn.net/?f=%5Cfrac%7Bz%7D%7B2%7D%20%2B%20%5Cfrac%7By%7D%7B3%7D%20%2B%5Cfrac%7Bx%7D%7B4%7D%3D%2065)
--- 4 years ago
Required
Their current age
![z - 4 = 4(x - 4)](https://tex.z-dn.net/?f=z%20-%204%20%3D%204%28x%20-%204%29)
Open bracket
![z -4 = 4x-16](https://tex.z-dn.net/?f=z%20-4%20%3D%204x-16)
Make z the subject
![z = 4x-16+4](https://tex.z-dn.net/?f=z%20%3D%204x-16%2B4)
![z = 4x-12](https://tex.z-dn.net/?f=z%20%3D%204x-12)
Multiply
by 12
![6z + 4y + 3x = 780](https://tex.z-dn.net/?f=6z%20%2B%204y%20%2B%203x%20%3D%20780)
Substitute
in ![6z + 4y + 3x = 780](https://tex.z-dn.net/?f=6z%20%2B%204y%20%2B%203x%20%3D%20780)
![6(4x - 12) + 4y + 3x = 780](https://tex.z-dn.net/?f=6%284x%20-%2012%29%20%2B%204y%20%2B%203x%20%3D%20780)
![24x - 72 + 4y + 3x = 780](https://tex.z-dn.net/?f=24x%20-%2072%20%2B%204y%20%2B%203x%20%3D%20780)
Collect like terms
![24x + 3x + 4y = 780+ 72](https://tex.z-dn.net/?f=24x%20%2B%203x%20%2B%204y%20%20%3D%20780%2B%2072)
![27x + 4y = 852](https://tex.z-dn.net/?f=27x%20%2B%204y%20%20%3D%20852)
Substitute
in ![\frac{x + y + z}{3} = 53](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%2B%20y%20%2B%20z%7D%7B3%7D%20%3D%2053)
![\frac{x + y + 4x - 12}{3} = 53\\](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%2B%20y%20%2B%204x%20-%2012%7D%7B3%7D%20%3D%2053%5C%5C)
Multiply through by 3
![x + y + 4x - 12 = 159](https://tex.z-dn.net/?f=x%20%2B%20y%20%2B%204x%20-%2012%20%3D%20159)
Collect like terms
![x + 4x + y = 159+12](https://tex.z-dn.net/?f=x%20%2B%204x%20%2B%20y%20%20%3D%20159%2B12)
![5x + y = 171](https://tex.z-dn.net/?f=5x%20%2B%20y%20%20%3D%20171)
Make y the subject
![y = 171 - 5x](https://tex.z-dn.net/?f=y%20%3D%20171%20-%205x)
Substitute
in ![27x + 4y = 852](https://tex.z-dn.net/?f=27x%20%2B%204y%20%20%3D%20852)
![27x + 4(171 - 5x) = 852](https://tex.z-dn.net/?f=27x%20%2B%204%28171%20-%205x%29%20%3D%20852)
![27x + 684 - 20x = 852](https://tex.z-dn.net/?f=27x%20%2B%20684%20-%2020x%20%3D%20852)
Collect like terms
![27x - 20x = 852-684](https://tex.z-dn.net/?f=27x%20%20-%2020x%20%3D%20852-684)
![7x = 168](https://tex.z-dn.net/?f=7x%20%3D%20168)
Divide by 7
![x = 24](https://tex.z-dn.net/?f=x%20%3D%2024)
Solve for y in ![y = 171 - 5x](https://tex.z-dn.net/?f=y%20%3D%20171%20-%205x)
![y =171 -5*24](https://tex.z-dn.net/?f=y%20%3D171%20-5%2A24)
![y =171 -120](https://tex.z-dn.net/?f=y%20%3D171%20-120)
![y =51](https://tex.z-dn.net/?f=y%20%3D51)
Solve for z in ![z = 4x-12](https://tex.z-dn.net/?f=z%20%3D%204x-12)
![z = 4 * 24- 12](https://tex.z-dn.net/?f=z%20%3D%204%20%2A%2024-%2012)
![z = 96- 12](https://tex.z-dn.net/?f=z%20%3D%2096-%2012)
![z = 84](https://tex.z-dn.net/?f=z%20%3D%2084)
These questions are all of the same type: division. They ask to find how many of a number can fit in another number.
As for question 5, there are 42 pounds of dog food, and
pound of dog food is used for each feeding. To find the number of times Mr. Lash can feed his animals, divide 42 by
. The answer is 48.
Solving the rest of the questions by this method, here are the answers. If you wish you can do them yourself to verify your understanding.
6) 12
7) 4
8) 8
9) 2
Note: in question 9, the question is in reverse order compared to the other questions.
Answer:
n = 6
Step-by-step explanation:
First we would plug the values with n, starting with 4.
![3*4 + 4*4 = 28](https://tex.z-dn.net/?f=3%2A4%20%2B%204%2A4%20%3D%2028)
So A. is not an option
Now we try 2.
![3*2 + 4*2 = 14](https://tex.z-dn.net/?f=3%2A2%20%2B%204%2A2%20%3D%2014)
B is NOT an option
Now we try 7
![3*7 + 4*7 = 49](https://tex.z-dn.net/?f=3%2A7%20%2B%204%2A7%20%3D%2049)
Now we try 21
![3*21 + 4*21 = 147](https://tex.z-dn.net/?f=3%2A21%20%2B%204%2A21%20%3D%20147)
Now we check what was closest...7
so we try numbers less than 7
n is = to 6