There are 3 red marbles and 8 blue marbles in a bag. (a) What is the ratio of all marbles in the bag to blue marbles? (b) What is the ratio of blue marbles to red marbles?
Understand the Problem
The question asks to find the ratio of marbles in a bag. First, calculate the total number of marbles. Then, determine both ratios of (a) all marbles to blue marbles and (b) blue marbles to red marbles, in that order.
Answer
(a) $11:8$ (b) $8:3$
Answer for screen readers
(a) $11:8$ (b) $8:3$
Steps to Solve
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Calculate the total number of marbles. To find the total number of marbles in the bag, add the number of red marbles and the number of blue marbles. $3 + 8 = 11$ There are 11 marbles in total.
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Find the ratio of all marbles to blue marbles. The ratio of all marbles to blue marbles is the total number of marbles divided by the number of blue marbles. $11:8$
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Find the ratio of blue marbles to red marbles. The ratio of blue marbles to red marbles is the number of blue marbles divided by the number of red marbles. $8:3$
(a) $11:8$ (b) $8:3$
More Information
Ratios are used to compare the quantities of two or more items. They can be written in several ways, including using a colon (like in this problem) or as a fraction.
Tips
A common mistake is to reverse the order of the ratio. For example, for part (a), giving the ratio of blue marbles to all marbles instead of all marbles to blue marbles. Always double-check that the order in the ratio matches the order specified in the problem.
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