SOLUTION: Darren had some round and square magnets. The ratio of the number of round magnets to the number of square magnets was 1:5. The ratio of the number of big magnets to the number of

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Darren had some round and square magnets. The ratio of the number of round magnets to the number of square magnets was 1:5. The ratio of the number of big magnets to the number of       Log On


   

Question 1204019: Darren had some round and square magnets. The ratio of the number of round magnets to the number of square magnets was 1:5. The ratio of the number of big magnets to the number of small magnets was 5:3. 60% of the square magnets were big magnets. What was the ratio of the number of big square magnets to the number of big round magnets?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
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let
round magnets be r
square magnets s
the number big magnets be x
the number of small magnets be y

if the ratio of the number of round magnets to the number of square magnets was 1%3A5, we have
r%3As=1%3A5
5r=1s
s=5r.....eq.1
The ratio of the number of big magnets to the number of small magnets was 5%3A3.
x%3Ay=5%3A3
3x=5y
x=5y%2F3
60%=0.60 of the square magnets were big magnets. =>0.60s=x =>s=x%2F0.60
go to eq.1, substitute s=x%2F0.60
s=5r.....eq.1
x%2F0.60=5r
x%2Fr=5%2A0.60
x%2Fr=3
x%2Fr=3%2F1
the ratio of the number of big square magnets to the number of big round magnets is 3%3A1

Answer by greenestamps(13203) About Me  (Show Source):
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Let x be the number of round magnets.

Then 5x is the number of square magnets. (round:square = 1:5)

The total number of magnets is then 6x.

big:small = 5:3, so 5/8 of the magnets are big and 3/8 are small.

That means the number of big magnets is (5/8)(6x) = (15/4)x and the number of small magnets is (3/8)(6x) = (9/4)x.

At this point, we can scale our numbers up by a factor of 4 so we don't have to deal with the fractions:

4x = number of round magnets
20x = number of square magnets
15x = number of big magnets
9x = number of small magnets

60% of the square magnets are big magnets, so

(.6)(20x) = 12x is the number of big square magnets

Then the number of big round magnets is 15x-12x = 3x.

And the ratio of big square magnets to big round magnets is 12x:3x = 4:1

ANSWER: 4:1