10 = 2x5
4 = 2x2
LCM + 2x2x5 = 20 <=== smallest number of bracelets and hair bow to buy
The missing number is 6. 3.6-.65 = 2.95
3.6 - 2.95 = .65
Hope it helps ;)))
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.
<span>Equation at the end of step 1 :</span><span><span> (((4•(y2))-5y)+(3y-(7•(y2))))-((2y2+6y)-5)
</span><span> Step 2 :</span></span><span>Equation at the end of step 2 :</span><span><span> (((4•(y2))-5y)+(3y-7y2))-(2y2+6y-5)
</span><span> Step 3 :</span></span><span>Equation at the end of step 3 :</span><span> ((22y2 - 5y) + (3y - 7y2)) - (2y2 + 6y - 5)
</span><span> Step 4 :</span><span> Step 5 :</span>Pulling out like terms :
<span> 5.1 </span> Pull out like factors :
<span> -5y2 - 8y + 5</span> = <span> -1 • (5y2 + 8y - 5)</span>
I hope tht help
