# Ratio word problem: What fraction of the original counters remain in the bag

• MHB
• Jessica15
In summary, the conversation discusses a word equation involving the removal of red and blue counters from a bag. After removing 1/4 of the red counters and 3/5 of the blue counters, the question is posed about the fraction of the original counters that remain in the bag. Through calculations and examples, it is determined that 11/17 of the original counters remain.
Jessica15
I have a word equation i cannot figure out! anyone have any ideas?

There is a large bag of red and blue counters. One red and one blue counter are removed from the bag. This process is repeated until 1/4 of the red counter and 3/5 of the blue counters have been removed. What fraction of the original counters remain in the bag?

Im stumped!
I've written that:

Red - n = 3/4 Red
blue - n = 2/5 blue
n is the number of counters removed as it the same number removed from both.

therefore n = 1/4red and n = 3/5 blue. therefore 1/4 red = 3/5 blue. if you cross multiply that you get that 5 red = 12 blue... I don't know how that helps!

n = (3/5)B
----------- $\implies$ 1 = (12B)/(5R) $\implies$ B/R = 5/12 ... 5 blue, 12 red, 17 total
n = (1/4)Rif n = 3, 3 blue counters are removed = 3/5 ofthe original 5 ... 3 red counters are removed = 1/4 of the original 12

2 blue and 9 red counters remain ... 11/17 of the original counters remain

Hint:
r = 24, b = 10, n = 6

r: 24 - 6 = 18 : 3/4 left
b: 10 - 6 = 04 : 2/5 left

B/r = 5/12 = 10/24 = 15/36 = ...

## What is a ratio word problem?

A ratio word problem is a type of math problem that involves using ratios to compare two quantities. It typically involves finding the relationship between two numbers or quantities and using that relationship to solve the problem.

## What is a fraction?

A fraction is a numerical representation of a part of a whole. It consists of a numerator (the number on top) and a denominator (the number on the bottom). Fractions can be used to represent a portion or share of something, such as the number of counters in a bag.

## How do you solve a ratio word problem?

To solve a ratio word problem, you first need to identify the quantities being compared and the relationship between them. Then, you can set up a proportion or use equivalent fractions to find the missing value. Finally, check your answer to make sure it makes sense in the context of the problem.

## What is the original amount in a ratio word problem?

The original amount in a ratio word problem refers to the starting quantity or total number of items before any changes or adjustments are made. In the context of the given problem, it would be the total number of counters in the bag before any were removed.

## How do you find the fraction of the original counters that remain in the bag?

To find the fraction of the original counters that remain in the bag, you would first need to determine the number of counters that were removed from the bag. Then, you can use this number to set up a proportion or find the equivalent fraction to represent the remaining counters. The resulting fraction would be the answer to the problem.

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