Balancing Problem - Part 1

Let us denote the squares as x, stars as y, and circles as z.

Therefore, $3z = 4x.$

Or, $z = \dfrac{4x}{3}$

Or, $2z = \dfrac{8x}{3}$ ,which is the value of 2 circles.

And, $3y = 2x.$

Or, $y = \dfrac{2x}{3}$ , which is the value of 1 star.

Therefore no. of stars balancing 2 circles is given by, $\displaystyle\frac {\dfrac{8x}{3}} {\dfrac{2x}{3}}=\boxed{4}$

6 stars= 4 squares

6 stars=3 circles

So, 2 stars= 1 circle(ratio)

So doing ratio, 4 stars=2 circles

being as there are half as many squares on the first balanced beam, and 4 on the second, one can deduct that each star is equal to half a circle. therefore one would require 4 stars to balance against 2 squares.

X=square Y=stars Z=Circles
2X=3Y
4X=3Z
4X=6Y
3Z=6Y
Z=2Y
2Z=4Y
4 stars

From second fig 4 Square: 3 circle :: x squares : 2 circles So 2 circles would be balanced by 8/3 squares From first fig So again, 3 star: 2 squares::y stars: 8/3 squares There fore no. of stars required to balance 2 circles are 4 stars!! simple!!!

X=square Y=stars Z=Circles 2X=3Y 4X=3Z 4X=6Y 3Z=6Y Z=2Y 2Z=4Y 4 stars

2 squares = 3 stars

4 squares = 6 stars

6 stars = 3 circles

so 2 circles = 4 stars

(3 stars/2 squares)*(4 squares/3 circles) = 2 stars/circle

2 circles*(2 stars/circle) = 4 stars

^_^

All those variables!

I just saw that 4 squares equaled 3 circles. That meant that 2 squares (which from the top scaled equaled 3 stars) equaled 1.5 circles. That meant that 3 stars equalled 1.5 circles.

1 star equals 1/2 circle. Which means that to get two circles, you would need 4 stars.

X=star Y=square Z=circle then 3X=2Y & 4Y=3Z,
Y=3/2 X,
4.3/2X=3Z,
2X=Z, so that 2Z=4X

. All I did was notice that the circles weighed twice as much as the stars. 2 circles equals 4 stars

2 blocks is 3 stars then 4 blocks is 6 stars and 3 circles equils 6 stars because 6 stars is 4 blocks then you have a ratio of 1 to 3 so 2 circles equils 4 stars

2 squares = 3 stars
4 squares = 3 circles
i.e 3 circles = 4 squares = 2 * 3 stars = 6 stars
i.e 2 circles = 4 stars