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
Answer:
± 60
Step-by-step explanation:
aₙ = a₁ * rⁿ⁻¹
a₇ = 30 = a₁ * r⁷⁻¹ = a₁ * r⁶ (1)
a₅ = 120 = a₁ * r⁵⁻¹ = a₁ * r⁴ (2)
(1)/(2): 30/120 = 1/4 = r²
r = ± 1/2 or ± 0.5
a₁ = a₇/r⁶ = 30/0.5⁶ = 1920
a₆ = 1920 * (± 1/2)⁶⁻¹ = 1920 * ± 1/32 = ± 60
When adding/subtracting fractions you need a common denominator, but you already have one, which is x-3. So in general:
a/c-b/c=(a-b)/c so you just have:
(2x-6)/(x-3) now if you factor 2 from the numerator
2(x-3)/(x-3) the (x-3)s cancel out leaving
2
However! Note that division by zero is undefined, so x cannot equal 3. (because both original fractions had denominators of x-3)
What this all means is that that expression will equal 2 for all real values of x other than 3.
