Answer:
6
Step-by-step explanation:
Let n be unknown divisor and a be the same remainder, then
![63=q_1\cdot n+a\\ \\45=q_2\cdot n+a\\ \\69=q_3\cdot n+a](https://tex.z-dn.net/?f=63%3Dq_1%5Ccdot%20n%2Ba%5C%5C%20%5C%5C45%3Dq_2%5Ccdot%20n%2Ba%5C%5C%20%5C%5C69%3Dq_3%5Ccdot%20n%2Ba)
Subtract a from all equalities:
![63-a=q_1\cdot n\\ \\45-a=q_2\cdot n\\ \\69-a=q_3\cdot n](https://tex.z-dn.net/?f=63-a%3Dq_1%5Ccdot%20n%5C%5C%20%5C%5C45-a%3Dq_2%5Ccdot%20n%5C%5C%20%5C%5C69-a%3Dq_3%5Ccdot%20n)
Subtract them:
![63-45=(q_1-q_2)n\Rightarrow 18=(q_1-q_2)n\\ \\69-63=(q_3-q_1)n\Rightarrow 6=(q_3-q_1)n\\ \\69-45=(q_3-q_2)n\Rightarrow 24=(q_3-q_2)n](https://tex.z-dn.net/?f=63-45%3D%28q_1-q_2%29n%5CRightarrow%2018%3D%28q_1-q_2%29n%5C%5C%20%5C%5C69-63%3D%28q_3-q_1%29n%5CRightarrow%206%3D%28q_3-q_1%29n%5C%5C%20%5C%5C69-45%3D%28q_3-q_2%29n%5CRightarrow%2024%3D%28q_3-q_2%29n)
The greatest number is 6. When you divide numbers 63, 45, 69 by 6, you'll get remainders 3, 3, 3, respectively.
Answer:
![y = 75 + 10x](https://tex.z-dn.net/?f=y%20%3D%2075%20%2B%2010x)
Step-by-step explanation:
Given
New Video Games
![Cost = \$25](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%2425)
![Number = 3](https://tex.z-dn.net/?f=Number%20%3D%203)
Used Video Games
![Cost = \$10](https://tex.z-dn.net/?f=Cost%20%3D%20%5C%2410)
![Number = x](https://tex.z-dn.net/?f=Number%20%3D%20x)
Required
Determine the amount spent (y)
First, we need to determine the total spent on new games
1 new game = $25
3 new games will be: 3 * $25
Next, we determine the total spent on old games
1 used game = $10
x used games will be: x * $10
So, total amount y, is:
![y = 3 * 25 + x * 10](https://tex.z-dn.net/?f=y%20%3D%203%20%2A%2025%20%2B%20x%20%2A%2010)
![y = 75 + 10x](https://tex.z-dn.net/?f=y%20%3D%2075%20%2B%2010x)
Look for the biggest number that they can all be divided by, and if there is a variable see if they can all have at least one of that variable taken away, so for example, in the numbers 20, 50, and 65 the greatest common factor is 5, there is no variable so you could just say 5 (4 + 10 + 13), however let’s say you came across 20y + 50y^4 + 65y^2, they all have at least one variable to take from so in this case you would factor using 5y, and it would look like this 5y (4 + 50y^3 + 65y). I hope that made sense, please tell me if you need further explanation and I’ll try my best to put it in an easier or more descriptive way.
Answer:
$365.70
Step-by-step explanation:
The formula to find this is ![y = a(1+r)^t\\](https://tex.z-dn.net/?f=y%20%3D%20a%281%2Br%29%5Et%5C%5C)
For this, a is the initial amount, r is the growth rate percentage (but displayed as a decimal), and t is time.
So to solve, you would do
![y = 300(1+0.02)^10\\y = 300(1.02)^10\\y = 365.698325998\\OR\\y = $365.7 in interest](https://tex.z-dn.net/?f=y%20%3D%20300%281%2B0.02%29%5E10%5C%5Cy%20%3D%20300%281.02%29%5E10%5C%5Cy%20%3D%20365.698325998%5C%5COR%5C%5Cy%20%3D%20%24365.7%20in%20interest)