![\left[\begin{array}{ccc}1&3&7\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%267%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
multiply 2nd row by -1 and add to first row
![\left[\begin{array}{ccc}0&2&6\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%262%266%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
divide the 1st row by 2
![\left[\begin{array}{ccc}0&1&3\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%263%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
multiply the first row by -1 and add to 2nd row
![\left[\begin{array}{ccc}0&1&3\\1&0&-2\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%263%5C%5C1%260%26-2%5Cend%7Barray%7D%5Cright%5D%20)
now we know
y+3=0
x-2=0
therefor
y=-3
x=2
Set of equations that can be used to calculate rate for each plumber:
2A+8B+8C = 1,400 --- (1)
4A+7B+10C = 1,660 --- (2)
3A+9B+9C = 1,660 --- (3)
------------------------------------
2*(1) - (2)
------------------------------------
4A+16B+16C = 2,800
4A+7B+10C = 1,660 -
------------------------------------
9B+6C = 1,140 --- (4)
------------------------------------
3(2) -4(3)
-----------------------------------
12A+21B+30C = 4,980
12A+36B+36C = 6,600 -
-----------------------------------
-15B-6C = -1,620 --- (5)
------------------------------------
(4) + (5)
------------------------------------
9B+6C = 1140
-15B-6C = -1620 +
-------------------------------------
-6B = -480 => 6B = 480 => B = 480/6 = 80
-------------------------------------------------------
Using (4), 9(80)+6C = 1140
720+6C = 1140 => 6C = 1140-720 = 420 => C = 420/6 = 70
------------------------------------------------------------------------------
Using (1), 2A+8(80)+8(70) = 1400
2A+640+560 =1400 => 2A = 1400-640-560 = 200 => A = 200/2 = 100
----------------------------------------------------------------------------------------------
The rates are:
A = $100
B = $80
C = $70
--------------------------------
On Thursday, number of calls: A = 4 hrs, B = 6 hrs, C = 3 hrs
Money earned = 4*100+6*80+3*70 = $1,090
S + a = 300...s = 300 - a
8s + 12a = 3200
8(300 - a) + 12a = 3200
2400 - 8a + 12a = 3200
-8a + 12a = 3200 - 2400
4a = 800
a = 800/4
a = 200 <==== 200 adult tickets
s = 300 - a
s = 300 - 200
s = 100 <=== 100 student tickets
It takes 2 hours to complete 10
Laps.
48/4 is 12 so it’s it 12 minutes a lap
12x10 is 120 which equals out to 2 hours
10 x 1 =10 0 x 0 =90 grorgi6
