The number of yellow counters in the bag Jamal has got for this case is obtained being 96
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given that:
- The bag initially had 36% of red counters and rest of the counters being yellow in color.
- Later was added 50 blue counters.
- The number of blue counter in the bag is 25% of all the counters in the bag.
Let the initial number of counters in the bag be 'x'
Then, 36% of x is:
[tex]\text{Number of red counters} = \dfrac{x}{100} \times 36 = 0.36 \times x[/tex]
Rest of them are yellow, so we get:
[tex]\text{Number of yellow counters} = x - \dfrac{x}{100} \times 36 = x(1-0.36) = 0.64 \times x[/tex]
Now, adding 50 blue counters make:
Total count of counters in bag = [tex]x + 50[/tex]
25% of this count is blue, and we know its 50. Thus, we get:
25% of (x+50) = 50
or
[tex]\dfrac{x+50}{100} \times 25 =50\\\\x+50 = 4 \times 50\\\\x = 200-50 = 150[/tex]
Thus, there were 150 coutners in the bag, initially.
The number of yellow counters is:
[tex]\text{Number of yellow counters} = 0.64 \times x = 0.64 \times 150 = 96[/tex]
Thus, the number of yellow counters in the bag Jamal has got for this case is obtained being 96
Learn more about percent here:
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