School-Safe Puzzle Games

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

34 Comments to “Balance the Scale Picture Puzzle”

1. Maya | Guest

The answer in 2 yellow hearts.. one Yellow heart is equal to 3green hearts and one red heart

2. Mark W | Guest

1 yellow = 2 red = 6 green

So 2 yellows are needed to balance scale #3.

3. PMK | Guest

2 Yellow Hearts

4. rajjo | Guest

2 yellow hearts

5. jason | Guest

2 yellows

6. Shawn | Guest

2 yellow hearts

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

7. 2D | Guest

3 for sure ^^

8. Mario | Guest

2 yellow hearts are needed.

1 Yellow = 2 Red
1 Red = 3 Green

9. Elizabeth | Guest

2 yellow.

10. Rick | Guest

Where do I find the answers?

11. Jay | Guest

2 yellow hearts…

12. suineg | Guest

I 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.

13. Ian | Guest

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

14. Rick | Guest

2 yellows

15. John Lewis Highsmith | Guest

2 yellow will do the job.

And the second diagram is not needed.

16. think | Guest

from 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.

17. Sanjay | Guest

The 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.

18. Jonathan Pantiesbrough | Guest

You need two yellow hearts.

Two red hearts = One yellow heart.
Six green hearts = One yellow heart.

19. RK | Profile

Rick- 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

20. GC | Guest

Ans: 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

21. blake | Guest

2 yellow

22. Deejam | Guest

From 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

23. Daniel | Guest

Two.

24. stefan | Guest

I 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.

25. JasonJ | Guest

2 Yellow.

26. Joe | Guest

2r+y=3r+3g
y=r+3g

3y=6r
y=2r
r+3g=2r
3g=r

6g=2r

4r=2y

2 yellow hearts.

27. Mudit | Guest

2 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

28. Sal | Guest

You 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.

29. RK | Profile

30. Nayan Shah | Guest

2 yellow hearts.

31. Abhishek Verma | Guest

it was a really simple problem..

32. Deb | Guest

R= 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

33. Seegers, Wayne » Blog Archive » Balance scales pictures | Guest

[…] 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 … […]