During an amorous struggle, the lady's pearls broke. Half of the pearls fell onto the floor, a fourth rolled under a chair, a sixth fell into her lap, and three pearls remained on the strain. How many pearls were there originally on the strand?
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To determine the original number of pearls on the strand, let's go step by step and add up the fractions:
1. Half of the pearls fell onto the floor: This means that half of the pearls remained on the strand. Let's represent the original number of pearls on the strand as "x." So, after half fell, we have x/2 pearls remaining.
2. A fourth rolled under a chair: This means that a fourth of the original number of pearls remained on the strand after the first incident. So, after a fourth rolled under a chair, we have (x/2) * (3/4) = 3x/8 pearls remaining.
3. A sixth fell into her lap: This means that a sixth of the original number of pearls remained on the strand after the second incident. So, after a sixth fell into her lap, we have (3x/8) * (5/6) = 5x/16 pearls remaining.
4. Three pearls remained on the strand: This means that 3 pearls were left after the third incident. So, we have 5x/16 = 3.
To find x, we will solve for it:
5x/16 = 3
Multiplying both sides by 16, we have:
5x = 3 * 16
5x = 48
Dividing both sides by 5, we get:
x = 48/5
Therefore, originally, there were 48/5 or 9.6 pearls on the strand. Since we cannot have a fraction of a pearl, we can conclude that there were 9 pearls originally on the strand.
Is the fourth included in those that fell on the floor? Was there a fifth pearl?
If the first answer is no and the second yes, the other half of the pearls = 1 + 1 + 1 + 3 = 6
When it says fourth and fifth, it refers to fraction, not whole numbers. So the formula is 3+ 1/6x +1/5x + 1/2x
and the answer is 30 which is calculated by figuring the LCM