00:01
Okay, so i see that you need help with this problem.
00:02
And it says a biologist has placed three strands of bacteria, denoted 1, 2, and 3, in a test tube, where they will feed upon three different storage sources, a, b, and c.
00:15
Suppose that 400 units of food a, so this is 400 units, 280 units of b, and 480 units of c, are placed in a test tube each day.
00:34
And the data on daily food consumption by the bacteria in units per day are shown in the table.
00:39
About how many bacteria of each strain can coexist in the test tube and consume all of the food.
00:45
So i'm going to do bacteria 1 strain is x, bacteria 2 strain is y, and bacteria 3 strand is z.
00:58
So i'm going to have my first for food a, x plus 2y equals 400.
01:10
Then for food b is 2x plus z equals 280.
01:19
And then i have food c being x plus y plus 2z equals 480.
01:31
And so now what i'm going to do is i'm going to solve for this.
01:39
So i'm going to solve here for x, or actually i'm going to solve here for x.
01:46
Nope, i'm going to solve for, so i have 2yz.
01:51
And if i solve for x for this one, i'll get a y and a z.
01:59
And if i solve for a y, i'll get an x and a z.
02:03
Okay, so i'm going to solve for this one for y.
02:05
So i have y equals negative 2z minus x plus 480.
02:22
So then i'm going to say, okay, well, x plus 2 multiplied by the quantity of negative 2z minus x plus 480 equals 400.
02:40
Oh, i put the zero on the 480.
02:42
Okay, so then i have x minus 4z minus 2x plus 480 times 2 is 960 equals 400.
03:03
So then i have, i'm going to combine like terms.
03:05
So i'll combine this x and this negative 2x to get negative x minus 4z and i'll subtract 960 from both sides.
03:16
Okay, that does not look like a 960.
03:19
And so negative 960 plus 400 is a negative 560 and then equals negative 560.
03:38
And then what i'm going to do is, i'm going to take this equation right here.
03:45
And i have a positive 2x plus z equals 280.
03:53
And what i'm going to do is, i'm going to now multiply this here equation by a positive 2, so i can solve for z...