We appreciate your visit to In a bag there are counters The counters are all either red blue or yellow The number of red counters blue counters and yellow counters. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
There are a total of 136 counters in the bag
Let's solve this step-by-step to find the total number of counters in the bag:
Representing the Ratio: We know the ratio of red, blue, and yellow counters is 4:5:8.
Connecting Ratio and Difference: We are given that the number of yellow counters (Y) is 24 more than the number of blue counters (B). We can represent this difference as:
Y = B + 24
Relating Ratio and Difference with a Common Denominator: Since the ratio uses multiples of 4, let's express the difference (24) as a multiple of 4 as well. We can see that 24 is 6 times 4. So, we can rewrite the difference as:
Y = B + (6 * 4)
Expressing Each Color Count using Ratio: We know the total ratio represents all the counters in the bag. Let T be the total number of counters. Then, based on the ratio, we can express the number of each color as:
Red (R) = (4/17) * T
Blue (B) = (5/17) * T
Yellow (Y) = (8/17) * T
Substituting Difference with Ratio Expression: Now, we can substitute the expression for Y (from step 3) into this equation:
(8/17) * T = (5/17) * T + (6 * 4)
Solving for the Difference Between Blue and Yellow: Simplifying the equation:
(3/17) * T = 24
Finding the Total Number of Counters (T): To find T, we can isolate it by multiplying both sides by the reciprocal of (3/17):
T = 24 * (17/3)
T = 136
There are a total of 136 counters in the bag
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