SOLUTION: Mike had some red and yellow marbles. If he exchanged 3/10 of his red marbles for yellow marbles, he would have 348 yellow marbles. If he exchanged 3/20 of his yellow marbles for t
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-> SOLUTION: Mike had some red and yellow marbles. If he exchanged 3/10 of his red marbles for yellow marbles, he would have 348 yellow marbles. If he exchanged 3/20 of his yellow marbles for t
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Question 1209142: Mike had some red and yellow marbles. If he exchanged 3/10 of his red marbles for yellow marbles, he would have 348 yellow marbles. If he exchanged 3/20 of his yellow marbles for the red marbles, he would have 204 yellow marbles. What fraction of the marbles that Mike had was red? Give your answer in its simplest form. Answer by ikleyn(52752) (Show Source):
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Mike had some red and yellow marbles. If he exchanged 3/10 of his red marbles for yellow marbles,
he would have 348 yellow marbles. If he exchanged 3/20 of his yellow marbles for the red marbles,
he would have 204 yellow marbles. What fraction of the marbles that Mike had was red?
Give your answer in its simplest form.
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Let R be the number of red marbles Mike had.
Let Y be the number of yellow marbles Mike had.
If he exchanged 3/10 of his red marbles for yellow marbles, he would have 348 yellow marbles.
It means
0.3R + Y = 348 (yellow marbles) (1)
If he exchanged 3/20 of his yellow marbles for the red marbles, he would have 204 yellow marbles.
It means
-0.15Y + Y = 204 (yellow marbles) (2)
From equation (2)
0.85Y = 204 ---> Y = 204/0.85 = 240.
So, Mike had 240 yellow marbles.
Now substitute Y = 240 into equation (2). You will get
0.3R = 348 - 240 = 108,
hence
R = 108/0.3 = 360.
So, Mike had 240 yellow marbles.
Total marbles Mike had was Y + R = 240 + 360 = 600.
Now the ratio = 360/600 = 3/5.
ANSWER. The fraction of red marbles Mike had was 3/5.
