There were some black beads and white beads ina box. The number
of black beads was 2/5 of the number of white beads. After 12 black
beads and 44 white beads were taken out of the box, the number of
black beads left in the box was 2/3 of the number of white beads left in
the box. How many beads were left in the box?
White beads --- w
black beads = (2/5)w
12 black taken our leaves (2/5)w - 12
44 white beads taken leaves w-44
(2/5)w - 12 = (2/3)(w-44)
times 15, the LCD
6w - 180 = 10w - 440
-4w = - 260
w = 65
number left in the box = (2/5)w-12 + w-44
sub in w = 65 to find how many are left
Well, this is quite a beady situation! Let's break it down using some colorful math jokes.
Let's call the number of white beads "W" and the number of black beads "B". According to your problem, we know that:
B = (2/5)W
After removing 12 black beads and 44 white beads, we have:
B - 12 = (2/3)(W - 44)
Now, let's spice it up with some puns. Why did the beads go on strike? They wanted to be independent, not mixed up in a box!
Now, let's substitute B with (2/5)W in the second equation:
(2/5)W - 12 = (2/3)(W - 44)
Let's simplify this a bit by getting rid of the fractions. You know what the beach told the wave? "Long time, no sea!" Let's multiply everything by 15 to make the fractions go away:
6W - 180 = 10(W - 44)
Now, let's distribute the 10:
6W - 180 = 10W - 440
To keep things balanced, we'll bring the W terms to one side and the number terms to the other side:
6W - 10W = -440 + 180
-4W = -260
Now, let's divide by -4:
W = -260 / -4
W = 65
Oh no, we have a negative number of white beads! That doesn't make sense in this situation. Let me try again.
Let's solve for B using B = (2/5)W:
B = (2/5) * 65
B = 26
Oh no, that doesn't work either! It seems like something went wrong somewhere along the way. I'm sorry, I must have gotten tangled up in my own jokes.
Let's start by assigning variables to the unknown quantities:
Let x be the number of white beads in the box initially.
Since the number of black beads was 2/5 of the number of white beads, the number of black beads initially can be represented as (2/5) * x.
After 12 black beads and 44 white beads were taken out of the box, the number of black beads left in the box was 2/3 of the number of white beads left.
Let's calculate the number of black beads left in the box:
Black beads left = (2/3) * (x - 44)
Now, let's use the information provided to solve the equation:
Initial number of black beads = (2/5) * x
Initial number of white beads = x
Black beads left = Initial number of black beads - 12
White beads left = Initial number of white beads - 44
Therefore, we can write the following equation:
(2/3) * (x - 44) = (2/5) * x - 12
To solve this equation, we can follow these steps:
1. Distribute (2/3) on the left side of the equation:
(2/3) * x - (2/3) * 44 = (2/5) * x - 12
2. Simplify both sides of the equation by multiplying the fractions:
(2/3) * x - (88/3) = (2/5) * x - 12
3. Multiply both sides of the equation by 15 to eliminate the fractions:
15 * [(2/3) * x - (88/3)] = 15 * [(2/5) * x - 12]
After simplifying, the equation becomes:
10x - 440 = 6x - 180
4. Subtract 6x from both sides of the equation and Add 440 to both sides:
10x - 6x = -180 + 440
After simplifying, the equation becomes:
4x = 260
5. Divide both sides of the equation by 4:
x = 65
So, there were initially 65 white beads in the box.
To find the number of beads left in the box, we can substitute the value of x in one of the given equations.
Black beads left = (2/3) * (x - 44)
Black beads left = (2/3) * (65 - 44)
Black beads left = (2/3) * 21
Black beads left = 14
Therefore, there are 14 black beads left in the box.
To find the total number of beads left in the box, we can add the number of black beads left and the number of white beads left:
Total beads left = Black beads left + White beads left
Total beads left = 14 + (65 - 44)
Total beads left = 14 + 21
Total beads left = 35
Therefore, there are 35 beads left in the box.
To solve this problem, let's assume the number of white beads in the box is "x".
According to the problem, the number of black beads is 2/5 of the number of white beads. So, we have:
Number of black beads = (2/5) * x
After 12 black beads and 44 white beads were taken out of the box, the number of black beads left is 2/3 of the number of white beads left. So, we have:
Number of black beads left = (2/3) * (x - 44) [x - 44 represents the number of white beads left]
Since we know that the number of black beads left is also the number of black beads minus 12, we can set up an equation:
(2/3) * (x - 44) = (2/5) * x - 12
Now, let's solve this equation to find the value of x, which represents the number of white beads in the box.
First, let's simplify the equation:
(2/3) * x - (88/3) = (2/5) * x - 12
Now, let's get rid of the fractions by multiplying both sides of the equation by the least common multiple (LCM) of 3 and 5, which is 15:
15 * [(2/3) * x - (88/3)] = 15 * [(2/5) * x - 12]
10x - 440 = 6x - 180
Next, let's collect like terms:
10x - 6x = -180 + 440
4x = 260
Finally, divide both sides of the equation by 4 to solve for x:
x = 260 / 4
x = 65
So, there were 65 white beads in the box initially.
Now, let's find the number of black beads initially:
Number of black beads = (2/5) * x
Number of black beads = (2/5) * 65
Number of black beads = 26
After 12 black beads and 44 white beads were taken out, the number of black beads left is:
Number of black beads left = 26 - 12
Number of black beads left = 14
And the number of white beads left is:
Number of white beads left = 65 - 44
Number of white beads left = 21
So, there are 14 black beads and 21 white beads left in the box.