Answer:
- Disitributive property.
- Addition property of equality.
Step-by-step explanation:
The complete exercise is attached.
For this exercise you need to remember the following properties:
1. The Distributive property states that:
![c(a+b)=ac+bc\\\\c(a-b)=ac-bc](https://tex.z-dn.net/?f=c%28a%2Bb%29%3Dac%2Bbc%5C%5C%5C%5Cc%28a-b%29%3Dac-bc)
2. The Addition property of equality states that:
![If\ a=b\ then\ a+c=b+c](https://tex.z-dn.net/?f=If%5C%20a%3Db%5C%20then%5C%20a%2Bc%3Db%2Bc)
Then, given the equation:
![4(2a + 3)= -3(a - 1) + 31 - 11a](https://tex.z-dn.net/?f=4%282a%20%2B%203%29%3D%20-3%28a%20-%201%29%20%2B%2031%20-%2011a)
You can identify that the first property John used was the Distributive property:
![(4)(2a) + (4)(3)= (-3)(a) +(-3)(- 1) + 31 - 11a\\\\8a+12=-3a+3+31-11a](https://tex.z-dn.net/?f=%284%29%282a%29%20%2B%20%284%29%283%29%3D%20%28-3%29%28a%29%20%2B%28-3%29%28-%201%29%20%2B%2031%20-%2011a%5C%5C%5C%5C8a%2B12%3D-3a%2B3%2B31-11a)
After combining like terms, you can identify that the next property he applied was the Addition property of equality, adding
to both sides of the equation:
![8a+12+(14)=-14a+34+(14)\\\\22a+12=34](https://tex.z-dn.net/?f=8a%2B12%2B%2814%29%3D-14a%2B34%2B%2814%29%5C%5C%5C%5C22a%2B12%3D34)
A palindrome is something that reads the same forwards and backwards.
If the number is a palindrome and it's between 300 and 400, then the
last digit must also be a ' 3 '.
So all we have left to fill in is the digit in the middle.
There are 10 possibilities for that one ... the digits ' 0 ' through ' 9 '.
So there are <em>10</em> palindromic numbers between 300 and 400.
Here is the solution.
Let s = small cups and l = large cups
s + l = 155
1.25s + 2.50l = 265
s = 155 - l
(now substitute)
1.25(155-l) + 2.50l = 265
193.75 - 1.25l + 2.50l = 265
1.25l = 71.25 (divide both sides by 1.25)
l = 57
Therefore there are 57 large cups sold
Next,
s + 57 = 155
s = 98
There are 98 small cups sold.
Hope this answers your question.