Grade 12th passAlgebra
- The number of ordered pairs (m,n),m,n€{1,2,.......50} such that 6n +9m is a multiple of 5.
- The number of ordered pairs (m,n),m,n€{1,2,.......50} such that 6n +9m is a multiple of 5.
2 Answers
Tony
I have done it with modulus(remainder) function. Modulus of 6^m will be 1 ^m anr that of 4^n is (-1)^n.
The key is to find a relation between m and n. For this question, if you take modulus 5, you get 1m +(-1)n = 1+(-1)n. The first thing to notice is that this is independent of m. Therefore, every value of m is possible. Thus, there are 50 possible m values. To make this equal to 0, you want n to be odd. Thus, there are 25 possible n values. Therefore, there are (50)(25)=1250 number of possible pairs.
Tony
Sry bro , by mistake in the above answer I have took the question as 6^m but it is 6^n.
Sry for that.Method is still same but bro just swap m with n wherever written in above answer!
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago