Hi there! To find the answer to that question, we can write and solve a proportion. Set it up like this: 240/x = 60/100. This is because we're looking for the whole and we already know the part, which is 240. Cross multiply the values in order to get 24,000 = 60x. Now, divide each side by 60 to isolate the variable. When you do, you get x = 400. You can check this by dividing and then multiplying that quotient by 100. 240/400 is 0.6 and 0.6 * 100 is 60. That makes 60%. There. 240 is 60% of 400.
The given equation
x/2 = y/3 = z/4
can be broken into three separate equations which I'll call equations (A), (B) and (C)
- x/2 = y/3 ..... equation (A)
- y/3 = z/4 .... equation (B)
- x/2 = z/4 .... equation (C)
We'll start off solving for z in equation (C)
x/2 = z/4
4x = 2z ... cross multiply
2z = 4x
z = 4x/2 ... divide both sides by 2
z = 2x
Now let's solve for y in equation (A)
x/2 = y/3
3x = 2y
2y = 3x
y = 3x/2
y = (3/2)x
y = 1.5x
The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.
We won't be using equation (B) at all.
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The key takeaway from the last section is that
Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:
(2x-y+5z)/(3y-x)
(2x-y+5(2x))/(3y-x) ..... plug in z = 2x
(2x-y+10x)/(3y-x)
(12x-y)/(3y-x)
(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x
(12x-1.5x)/(4.5x-x)
(10.5x)/(3.5x)
(10.5)/(3.5)
3
We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.
Answer:
36
Step-by-step explanation:
12 x 3 = 36
Answer:
ok cool?
Step-by-step explanation:
Let the yellow cubes be x
yellow = x
blue = 2x // Blue cubes is twice of yellow
Green = 8x // Green is four times of blue
Ratio:
Yellow : Blue : Green
1 : 2 : 8
P(Yellow) = 1/11
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Answer: The probability of getting a yellow cube is 1/11.
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