35. If b is a positive integer less than 400 and more than 100, then how many integer pairs (a,b) satisfy the equation a/b=2/9?
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To find out how many integer pairs (a, b) satisfy the equation a/b = 2/9, we can follow these steps:
1. Start by simplifying the equation to eliminate the fractions. Multiply both sides of the equation by 9, resulting in 9(a/b) = 2.
2. Multiply both sides of the equation by b to eliminate the fraction, yielding 9a = 2b.
3. Rearrange the equation to isolate a in terms of b: a = (2b)/9.
4. Now, we need to find the values of b that satisfy the given conditions - b is a positive integer less than 400 and greater than 100.
5. By substituting different values of b within the given range, we can find corresponding values of a.
Now, let's go through the process by substituting values of b and calculating the corresponding values of a.
Starting with b = 101:
a = (2 * 101) / 9 = 202 / 9 which is not an integer.
Next, b = 102:
a = (2 * 102) / 9 = 204 / 9 which is not an integer.
Continuing this process for all the values of b in the given range, we can find the corresponding values of a.
If we complete this process for each integer value of b between 100 and 400, we will find the values of a that satisfy the equation. The number of integer pairs (a, b) will be the count of these valid pairs.