A.) .4 of a balloon is left
To Check:
what I did was divide 172 by 27 and it is 6.37 rounded to ........6 is an equal number so I kept it and .4 will be left over after sharing equally.
B.) 17 more balloons are needs
To Check:
what I was multiply 27 by 7 because each student needs seven balloons and I got 189 after that I subtracted 172 from 189 (189-172=17)
to see how many more balloons are needed.
The answer is 4/3 thats the rate of change. up 3 over 4
Kelsey must spend less than or equal to $65.
The expression 5.50b+7.5 is correct
Kelsey able to purchase 10 books.
On the end Kelsey can spend $2.50 to purchase small present (calendar or book for notes)
Answer:
![x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]](https://tex.z-dn.net/?f=x_3%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%263%261%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
According to the given situation, The computation of all x in a set of a real number is shown below:
First we have to determine the
so that 
![\left[\begin{array}{cccc}1&-3&5&-5\\0&1&-3&5\\2&-4&4&-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%265%26-5%5C%5C0%261%26-3%265%5C%5C2%26-4%264%26-4%5Cend%7Barray%7D%5Cright%5D)
Now the augmented matrix is
![\left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\2&-4&4&-4\ |\ 0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%265%26-5%5C%20%7C%5C%200%5C%5C0%261%26-3%265%5C%20%7C%5C%200%5C%5C2%26-4%264%26-4%5C%20%7C%5C%200%5Cend%7Barray%7D%5Cright%5D)
After this, we decrease this to reduce the formation of the row echelon
![R_3 = R_3 -2R_1 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&2&-6&6\ |\ 0\end{array}\right]](https://tex.z-dn.net/?f=R_3%20%3D%20R_3%20-2R_1%20%5Crightarrow%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%265%26-5%5C%20%7C%5C%200%5C%5C0%261%26-3%265%5C%20%7C%5C%200%5C%5C0%262%26-6%266%5C%20%7C%5C%200%5Cend%7Barray%7D%5Cright%5D)
![R_3 = R_3 -2R_2 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&5\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]](https://tex.z-dn.net/?f=R_3%20%3D%20R_3%20-2R_2%20%5Crightarrow%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%265%26-5%5C%20%7C%5C%200%5C%5C0%261%26-3%265%5C%20%7C%5C%200%5C%5C0%260%260%26-4%5C%20%7C%5C%200%5Cend%7Barray%7D%5Cright%5D)
![R_2 = 4R_2 +5R_3 \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&4&-12&0\ |\ 0\\0&0&0&-4\ |\ 0\end{array}\right]](https://tex.z-dn.net/?f=R_2%20%3D%204R_2%20%2B5R_3%20%5Crightarrow%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%265%26-5%5C%20%7C%5C%200%5C%5C0%264%26-12%260%5C%20%7C%5C%200%5C%5C0%260%260%26-4%5C%20%7C%5C%200%5Cend%7Barray%7D%5Cright%5D)
![R_2 = \frac{R_2}{4}, R_3 = \frac{R_3}{-4} \rightarrow \left[\begin{array}{cccc}1&-3&5&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&1\ |\ 0\end{array}\right]](https://tex.z-dn.net/?f=R_2%20%3D%20%5Cfrac%7BR_2%7D%7B4%7D%2C%20%20R_3%20%3D%20%5Cfrac%7BR_3%7D%7B-4%7D%20%20%5Crightarrow%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-3%265%26-5%5C%20%7C%5C%200%5C%5C0%261%26-3%260%5C%20%7C%5C%200%5C%5C0%260%260%261%5C%20%7C%5C%200%5Cend%7Barray%7D%5Cright%5D)
![R_1 = R_1 +3 R_2 \rightarrow \left[\begin{array}{cccc}1&0&-4&-5\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]](https://tex.z-dn.net/?f=R_1%20%3D%20R_1%20%2B3%20R_2%20%5Crightarrow%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-4%26-5%5C%20%7C%5C%200%5C%5C0%261%26-3%260%5C%20%7C%5C%200%5C%5C0%260%260%26-1%5C%20%7C%5C%200%5Cend%7Barray%7D%5Cright%5D)
![R_1 = R_1 +5 R_3 \rightarrow \left[\begin{array}{cccc}1&0&-4&0\ |\ 0\\0&1&-3&0\ |\ 0\\0&0&0&-1\ |\ 0\end{array}\right]](https://tex.z-dn.net/?f=R_1%20%3D%20R_1%20%2B5%20R_3%20%5Crightarrow%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%260%26-4%260%5C%20%7C%5C%200%5C%5C0%261%26-3%260%5C%20%7C%5C%200%5C%5C0%260%260%26-1%5C%20%7C%5C%200%5Cend%7Barray%7D%5Cright%5D)

![x = \left[\begin{array}{c}4x_3&3x_3&x_3\\0\end{array}\right] \\\\ x_3 = \left[\begin{array}{c}4&3&1\\0\end{array}\right]](https://tex.z-dn.net/?f=x%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4x_3%263x_3%26x_3%5C%5C0%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%20x_3%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%263%261%5C%5C0%5Cend%7Barray%7D%5Cright%5D)
By applying the above matrix, we can easily reach an answer