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?
total number ---- x
x/2 + x/4 + x/6 + 3 = x
multiply each term by 12, the LCD
6x + 3x + 2x + 36 = 12x
solve for x
To determine the original number of pearls on the strand, we need to add up the fractions of pearls that fell into each different location.
Let's start by adding up the fractions:
1/2 (fell onto the floor) + 1/4 (rolled under a chair) + 1/6 (fell into her lap) + 3 (remaining on the strand) = ?
To make it easier to add up the fractions, we need a common denominator. The smallest number that 2, 4, and 6 all divide into evenly is 12.
Now let's rewrite the fractions with the common denominator:
6/12 + 3/12 + 2/12 + 3 = ?
Adding up the numerators, we get:
(6 + 3 + 2) / 12 + 3 = 11/12 + 3
To add the fractions, we need to have the same denominators. We can rewrite 3 as 36/12, which has the common denominator of 12:
11/12 + 36/12 = 47/12
Since we can't have a fraction of a pearl, we need to find a whole number that is divisible by 12. The smallest number that satisfies this condition is 48.
So, there were originally 48 pearls on the strand before the amorous struggle.