A flock of geese on a pond was being observed continuously. At 1:00pm, 1/5 of the geese flew away. At 2:00pm, 1/8 of the geese that remained flew away. At 3:00pm, 3 times as many geese has had flown away at 1:00pm flew away, leaving 28 geese on the pond. At no other time did any geese arrive or fly away.
How would I set up the equation to find out how many flocks of geese were in the original flock?
1:00 -- 1/5 gone, leaving 4/5
2:00 -- 4/5 * 1/8 = 1/10 flew, leaving 4/5 - 1/10 = 7/10
3:00 -- 3 * 1/5 = 3/5 gone, leaving 1/10
x/10 = 28
so the original flock was 280 geese
Trying to do all that in a single equation is possible, but would be very cumbersome. Good luck with that effort.
Is there a different way to do it?
1:00 is 1/5 and that becomes 4/5
2:00 is 1/8 and that becomes 7/8
3:00 is 3x
The equation would equal to 28
Then what would the equation be by using 28, 3x, 7/8, and 4/5
Original flock = X geese.
1:00 PM : x - x/5 = 4x/5 remained.
2:00 PM: 4x/5 - 1/8 * 4x/5 = 4x/5 - 4x/40 = 32x/40 - 4x/40 = 7x/10 remained
3:00 PM: 7x/10 - 3x/5 = 7x/10 - 6x/10 = x/10 remained.
x/10 = 28.
X = 280 geese.
To set up the equation to find out how many flocks of geese were in the original flock, we need to define the variables involved.
Let's assume that the total number of geese in the original flock is represented by "x".
According to the given information, at 1:00 pm, 1/5 of the geese flew away. So, after 1/5 of the geese flew away, the number of remaining geese can be expressed as:
Remaining geese at 1:00 pm = x - (1/5)x = (4/5)x
At 2:00 pm, 1/8 of the geese that remained flew away. So, after 1/8 of the remaining geese flew away, the number of remaining geese can be expressed as:
Remaining geese at 2:00 pm = (4/5)x - (1/8)(4/5)x = (7/10)x
At 3:00 pm, 3 times as many geese that flew away at 1:00 pm flew away, leaving 28 geese remaining. So, the equation can be formed as:
(7/10)x - 3 * (1/5)x = 28
Now you can solve this equation to find the value of "x", which represents the total number of geese in the original flock.
Your terminology is rather opaque.
And what do you mean when you finally say
The equation would equal to 28
what equation? An equation is never "equal" to anything.