In preparation for a party, Heather fills a jar with gumdrops. Before the party begins, Erik sees the gum drop jar, he (hoping that no one will realize) takes one-third of the drops. Soon after sonia takes takes one-third of the gumdrops(she too, hopes that no one will notice). Finally, neel appears and like the others he takes one third of the gumdrops. if forty are left in the jar, how many did it originally contain?
There were x gumdrops at the start.
After Erik raided the jar, there were 2x/3 drops.
After Sonia, there were 4x/9 drops
After Neel, there were 8x/27, which was 40
So, 8x/27 = 40
x = 135.
check:
Erik got 1/3 * 135 = 45, leaving 90
Sonia got 1/3 * 90 = 30, leaving 60
Neel got 1/3 * 60 = 20, leaving 40
To determine the original number of gumdrops in the jar, we can work backwards using the information provided.
Let's assume that the original number of gumdrops in the jar is represented by "x".
First, Erik takes one-third of the gumdrops, so he leaves behind 2/3 of the original amount. This means there are (2/3)x gumdrops remaining.
Next, Sonia takes one-third of the remaining gumdrops, leaving behind 2/3 of the remaining amount. Therefore, there are (2/3)((2/3)x) = (4/9)x gumdrops left.
Finally, Neel takes one-third of the remaining gumdrops, leaving behind 2/3 of the remaining amount. So, we have (2/3)((4/9)x) = (8/27)x gumdrops remaining.
We are given that when Neel is done, there are 40 gumdrops left in the jar. Therefore, we have the equation (8/27)x = 40.
To solve for x, we can multiply both sides of the equation by (27/8):
x = 40 * (27/8)
x = 13.5 * 27
x = 364.5
Since we cannot have a fraction of a gumdrop, we round up to the nearest whole number.
So, the jar originally contained 365 gumdrops.