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Fractions and Proportions
Sarah has a bag of marbles containing 30% red marbles and 70% blue marbles. If she adds 20 more red marbles to the bag, what will be the new proportion of red marbles to blue marbles in the bag? Show your work.
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1 Reply
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Initially, Sarah’s bag has 30% red marbles and 70% blue marbles.
This means that if there were 100 marbles in total, 30 of them would be red and 70 would be blue.
Sarah adds 20 more red marbles to the bag.
the total number of red marbles becomes 30 + 20 = 50.
The total number of marbles initially was 100, but after adding 20 more red marbles,
the total number of marbles becomes 100 + 20 = 120.
So, out of the 120 marbles, we have 50 red marbles and the remaining 120 – 50 = 70 marbles are blue.
proportion of red marbles is calculated by the number of red marbles divided by the total number of marbles.
that is, 50/120
To express this as a percentage, we can calculate the proportion of red marbles by dividing the number of red marbles by the total number of marbles and then multiplying by 100.
Proportion of red marbles = (number of red marbles / total number of marbles) * 100
= (50 / 120) * 100
= 41.67%
proportion of blue marble is 100-41.67=58.33
Therefore, after adding 20 more red marbles, the new proportion of red marbles to blue marbles in the bag is approximately 41.67% red marbles and 58.33% blue marbles.