Grades 9-10 Video Solutions 2023-2023_9-10

Video Transcription

The letters a and b are to be replaced by positive integers so that the equation is correct. And how many different ways can this be done?  So first we can cross multiply and find that ab equals 35.  Then we know that 35 can be prime factorized as 5 times 7.  The constraints of our questions tells us that a and b are both positive integers.  So the only pairs that could satisfy the conditions where they multiply to 35 and are also positive integers is 1 and 35, 35 and 1, 5 and 7, and 7 and 5. Therefore our answer is 4.  Notice that in this question it was important the order in which that a and b were in  as 5 and 7 was a different answer than 7 and 5 because we're assigning numbers specifically to a and specifically to b.

Video Summary

The letters a and b are to be replaced by positive integers so that the equation is correct. And how many different ways can this be done? So first we can cross multiply and find that ab equals 35. Then we know that 35 can be prime factorized as 5 times 7. The constraints of our questions tells us that a and b are both positive integers. So the only pairs that could satisfy the conditions where they multiply to 35 and are also positive integers is 1 and 35, 35 and 1, 5 and 7, and 7 and 5. Therefore our answer is 4. Notice that in this question it was important the order in which that a and b were in as 5 and 7 was a different answer than 7 and 5 because we're assigning numbers specifically to a and specifically to b.

Keywords

positive integers

prime factorization

cross multiply

equation

integer pairs