Answer:
u+2b=22
Unicycles have one wheel and bicycles have two, so the coefficient of 2 should go before the variable representing each bike.
It should equal 22 because 15 represents the total number of seats and not wheels.
Step-by-step explanation:
Well, this problem is best solved by setting up a system of two linear equations.
A linear equation can be defined
y=mx+b
where
b=initial value (when x=0), and
m=rate of increase or decrease.
In the given example, the x-axis represents hour, and the y-axis, number of cells.
Chemical #1
initial value = b = 12000 cells
rate = m = -4000 / hr
The equation is therefore
y1=-4000x+12000......................(1)
Similarly, for chemical #2
initial value = b = 6000 cells
rate = m = -3000 / hr
The equation is therefore
y2=-3000x+6000 .......................(2)
The time the two will have an equal sized colony would represent the solution of the system of equations (1) and (2), i.e. when y1=y2
which means
-4000x+12000 = -3000x+6000
transpose and solve for x
4000x-3000x = 12000-6000
1000x=6000
x=6 hours.
At 6 hours from the start,
y=-4000x+12000 = -4000*6+12000 = -24000+12000 = -12000 cells
So the solution is x=6, y=-12000, or (6,-12000)
Physical interpretation
Since cells cannot have a negative number, the two are actually equal before six hours, when they are both zero.
Case 1: y=0 when x=3
Case 2: y=0 when x=2
Therefore, after three hours, both trials will have zero cells.
You have to judge whether to give the mathematical solution (x=6,y=-12000) or the physical interpretation (x=3, y=0) as the answer.
Hi there!
Since we have 2 variables in the given equation, and you only want to solve for one, the other will end up in your answer.
Step 1) Add 8y to both sides.
Step 2) Divide both sides by 6.
Final Answer -
Hope this helps! :D
