Patton is organizing his stamp collection into ab ook. He has 42 foreign stamps and 70 US stamps. He wants every page to have the same number of foreign stamps and the same number of US stamps. If he puts the greatest number of stamps on each page, how many pages will he use?
A.2
B.6
C.7
D.10
I thought the answer was 8. Because the GCM is 14 and for 42 stamps it would be 3 pages and for 70 stamps it would be 5 pages, so 5+3=8
2 pages
21 foreign and 35 US stamps on each page.
The answer is 7
To find the number of pages Patton will use, let's find the greatest common divisor (GCD) of 42 and 70.
Step 1: Find the prime factors of 42:
42 = 2 x 3 x 7
Step 2: Find the prime factors of 70:
70 = 2 x 5 x 7
Step 3: Determine the common prime factors:
The only common prime factor is 7.
Step 4: Calculate the GCD:
GCD(42, 70) = 7
Now, since Patton wants each page to have the same number of foreign stamps and the same number of US stamps, he will use the GCD (7) as the number of stamps on each page.
So, to find the number of pages, we divide the total number of stamps of each type by the GCD:
Foreign stamps: 42 / 7 = 6 pages
US stamps: 70 / 7 = 10 pages
Therefore, he will use the smaller number of pages, which is 6.
The correct answer is B. 6 pages.
To determine the number of pages Patton will use for organizing his stamp collection, we need to find the greatest common divisor (GCD) of 42 (foreign stamps) and 70 (US stamps).
Your reasoning of finding the GCD is correct. The GCD of 42 and 70 is 14.
Now, let's calculate the number of pages needed for each type of stamp.
For foreign stamps, dividing 42 by 14 (the GCD) gives us 3 pages.
For US stamps, dividing 70 by 14 (the GCD) gives us 5 pages.
Since we want to have an equal number of foreign stamps and US stamps on each page, we need to find the minimum number of pages that satisfy this condition.
To do this, we need to divide both the number of foreign stamps and US stamps by their GCD and then take the maximum of the two results.
In this case, the maximum value is 5 because we can fit 5 pages of US stamps on each page.
Therefore, Patton will use a total of 5 pages to organize his stamp collection, which means the answer is not 8.
Among the given options (A, B, C, D), the correct answer is C. 7 pages.