## Balance the Scale Picture Puzzle

How many yellow hearts are needed to balance scale #3?

hope this doesn’t turn out to be as difficult as the last scale balancing puzzle we posted…

How many yellow hearts are needed to balance scale #3?

hope this doesn’t turn out to be as difficult as the last scale balancing puzzle we posted…

Maya| Guest September 6th, 2007 - 2:07 amThe answer in 2 yellow hearts.. one Yellow heart is equal to 3green hearts and one red heart

Mark W| Guest September 6th, 2007 - 3:03 am1 yellow = 2 red = 6 green

So 2 yellows are needed to balance scale #3.

PMK| Guest September 6th, 2007 - 6:16 am2 Yellow Hearts

rajjo| Guest September 6th, 2007 - 6:22 am2 yellow hearts

jason| Guest September 6th, 2007 - 6:32 am2 yellows

Shawn| Guest September 6th, 2007 - 7:08 am2 yellow hearts

Only the information from scale #1 is required. 1 yellow = 3 green + 1 red

2D| Guest September 6th, 2007 - 11:10 am3 for sure

Mario| Guest September 6th, 2007 - 12:43 pm2 yellow hearts are needed.

1 Yellow = 2 Red

1 Red = 3 Green

Elizabeth| Guest September 6th, 2007 - 1:00 pm2 yellow.

Rick| Guest September 6th, 2007 - 1:03 pmWhere do I find the answers?

Jay| Guest September 6th, 2007 - 1:59 pm2 yellow hearts…

andrew| Guest September 6th, 2007 - 2:34 pm2

suineg| Guest September 6th, 2007 - 2:43 pmI think one possible answer is 2 yellow hearts, here is my explanation:

1) From balance scale 2 –> 3 Yhearts= 6 RHearts–> 1 YHeart= 2 Rhearts

2) From balance scale 1–> 2 RHearts+ 1 YHeart= 3 Rhearts + 3 GHearts, then from (1)–> 4 RHeart=3 RHearts + 3 GHearts–> 1 RHeart= 3 GHearts

3) From balance scale 3–> 2 RHearts+ 6 GHearts= ? YHearts—> then from (2)–>4 RHearts=? YHearts from (1) –>4 RHearts=2 YHearts.

Ian| Guest September 6th, 2007 - 3:26 pm2 yellow hearts.

the greens are 1/6 of the yellow and the red are 1/2 of the yellow

Rick| Guest September 6th, 2007 - 3:55 pm2 yellows

John Lewis Highsmith| Guest September 6th, 2007 - 4:09 pm2 yellow will do the job.

And the second diagram is not needed.

think| Guest September 6th, 2007 - 4:33 pmfrom scale 2 we can see that 1 yellow heart = two red hearts.

from scale 1 have have one yellow heart on the left taking two of the red hearts on the right side, and one red heart on the left taking the third red heart on the right. this leaves one read heart on the left and three green on the right, so 1 red heart = 3 green hearts.

in the final scale we have

2 red hearts = 1 yellow heart

6 green hearts == 6/3 = 2 red hearts == 1 yellow heart.

Therefore 2 yellow hearts are needed.

Sanjay| Guest September 6th, 2007 - 5:58 pmThe answer is 4 yellow hearts:

from scale#1: 2 red + 1 yellow = 3 red and 3 greens

so 1 yellow is equivalnet to 3 greens minus one red (or y = 3g – r)

from scale#2: 3 yellow = 6 reds or (3y = 6r, equivalent to y = 2r)

scale#3 needs to balance 6 greens and 2 red using yellow.

The number of yellow hearts you need to balance 2 reds is 1 yellow (from scale #2 eqn)

The number of yellow hearts you need to balance 6 greens is:

y=3g – r, so 3g = y + r. Multiplying by 2 on both sides:

6g = 2y + 2r, and we know 2r = y (from scale #2), so:

6g = 2y + y, so 6g = 3y. So need 3 yellows to balance 6 greens

Putting this together on scale#3:

6g + 2r = 3y + y

so need 4 yellow hearts to balance 6 greens and 2 reds.

Quite verbose, but thats how i thought of it.

Jonathan Pantiesbrough| Guest September 6th, 2007 - 6:33 pmYou need two yellow hearts.

Two red hearts = One yellow heart.

Six green hearts = One yellow heart.

RK| Profile September 6th, 2007 - 6:42 pmRick- answers get unmasked in 1-2 days usually. This gives everyone a chance to really try to solve the puzzle without giving in to the temptation to quickly scroll down and "cheat".

Usually multiple answers/explanations are submitted, which can go a long ways in helping others understand the problem & solution better. (For example, follow the above link to the earlier scale balance problem)

Occasionally there’s more than 1 answer, and this gets pointed out from time to time

GC| Guest September 6th, 2007 - 8:02 pmAns: 2 Yellow hearts. From (2) 1YH = 2RHs; from (1) then it is clear that 1 YH = 6 GHs. So, in (3) 6 GHs+2 RHs = 2 YHs

blake| Guest September 6th, 2007 - 10:23 pm2 yellow

Deejam| Guest September 6th, 2007 - 11:41 pmFrom figure 2 we get

1 Yellow = 2 Red

with this and from figure1

1 Red = 3 Green

So for balancing figure 3

2 Yellow needed

Daniel| Guest September 6th, 2007 - 11:43 pmTwo.

stefan| Guest September 7th, 2007 - 7:38 amI hope it’s ok to post my answer here..

I say ten yellows.

I get this because scale #2 shows that 1 yellow = 2 red.

Using that in #1 I replace the yellows with reds then subtract three reds from each side leaving 1 red = 3 greens.

In #3, replacing the 6 reds with 18 greens makes it 20 reds.

To balance 20 reds I need 10 yellows.

JasonJ| Guest September 7th, 2007 - 8:04 am2 Yellow.

Joe| Guest September 7th, 2007 - 1:55 pm2r+y=3r+3g

y=r+3g

3y=6r

y=2r

r+3g=2r

3g=r

6g=2r

4r=2y

2 yellow hearts.

Mudit| Guest September 7th, 2007 - 3:50 pm2 yellows are needed

Solution:

On the first scale, eliminate two reds from each side.

This shows that 1 yellow = 1 red and 3 greens

On the second scale, simple division shows that 1 yellow = 2 reds

*From this you can see that 1 red = 3 greens

On the third scale, substitute the 2 reds for 1 yellow, and the 6 greens for 1 yellow, and you are left with 2 yellows

Sal| Guest September 7th, 2007 - 6:12 pmYou actually can solve this without the second balance.

On the first scale, two red hearts on the left balance out two red hearts on the right, leaving one yellow heart on the left equal to three green and one red heart on the right.

Since one yellow heart = 3 green hearts and 1 red heart, it will take 2 yellow hearts to balance 6 green hearts and 2 red hearts.

RK| Profile September 8th, 2007 - 10:26 amAnswer: 2 yellow hearts

Nayan Shah| Guest September 11th, 2007 - 6:51 am2 yellow hearts.

Abhishek Verma| Guest September 20th, 2007 - 5:32 amanswer is 2 yellow hearts.

it was a really simple problem..

Deb| Guest October 13th, 2007 - 8:32 pmR= red hearts

Y= yellow hearts

G=green hearts

#1. 2R+1Y=3G+3R

R=3 Y=6 G=1

2(3)+6=3(1)+3(3)

6+6=3+9

12=12

#2. 3Y=6R

3(6)=6(3)

18=18

#3. x= amount of yellow hearts needed

6G+2R= xY

6(1)+2(3)=x(6)

6+6=x6

12=x6

12/6=x

2=x

2 YELLOW HEARTS ARE NEEDED

Seegers, Wayne » Blog Archive » Balance scales pictures| Guest August 17th, 2011 - 3:24 pm[...] Balance the Scale Picture Puzzle | Smart-Kit Puzzles and Games Sep 6, 2007 … How many yellow hearts are needed to balance scale #3? hope this doesn't turn out to be as difficult … [...]