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In Diana's stamp collection, \(\frac{4}{5}\) of the stamps are Canadian, and \(\frac{3}{7}\) of the Canadian stamps were issued before 1940. If 192 stamps in Diana's collection are Canadian stamps that were issued in 1940 or later, how many stamps in her collection are not Canadian?
A. 84
B. 88
C. 96
D. 104
E. 112
A. 84
B. 88
C. 96
D. 104
E. 112
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02 Mar 2024, 13:01
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Gprabhumir
We can use a 2*2 matrix to plot the information as shown below -
Attachment:
Screenshot 2024-03-03 012640.png [ 10.28 KiB | Viewed 8670 times ]
If 192 stamps in Diana's collection are Canadian stamps that were issued in 1940 or later
\(\frac{4}{5}*x - (\frac{3}{7}*\frac{4}{5}*x) = 192\)
\(\frac{4}{5}*x*(1-\frac{3}{7}) = 192\)
\(\frac{4}{5}*x*(\frac{4}{7}) = 192\)
\(x = 12 * 5 * 7\)
Number of stamps in her collection that are not Canadian = \(\frac{1}{5} * x = \frac{1}{5} * (12*5*7) = 12 * 7 = 84\)
Option A
04 Mar 2024, 23:35
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Remember that the 3/7 fraction is for Canadian stamps BEFORE 1940. The 192 figure, however, is for Canadian stamps AFTER 1940.
Basically, 4/7 of total Canadian coins is equal to 192 coins.
To find the total number of Canadian coins, take 192 and first divide it by 4 and then multiply it by 7. In a sense, you're trying to change 4/7 into 7/7.
• 192 / 4 = 48
• 48 x 7 = [(50 x 7) – 14] = 336
Now that we know 336 stamps is equal to 4/5 of all stamps (which accounts for all the Canadian stamps), the remaining 1/5 would have to be non-Canadian.
To get 1/5 of all stamps, simply take 336 (4/5 of all stamps) and divide it by 4.
336/4 = 84
A is your answer.
Basically, 4/7 of total Canadian coins is equal to 192 coins.
To find the total number of Canadian coins, take 192 and first divide it by 4 and then multiply it by 7. In a sense, you're trying to change 4/7 into 7/7.
• 192 / 4 = 48
• 48 x 7 = [(50 x 7) – 14] = 336
Now that we know 336 stamps is equal to 4/5 of all stamps (which accounts for all the Canadian stamps), the remaining 1/5 would have to be non-Canadian.
To get 1/5 of all stamps, simply take 336 (4/5 of all stamps) and divide it by 4.
336/4 = 84
A is your answer.
