Remainder

[dagr8est]

When the positive number m is dividied by 5, the remainder is 3. What is the remainder when 20m is divided by 25?

(Correct Answer = 10)

I did:

Let x = multiple of 5
Then m/5 = x/5+3/5
m = x+3
m-3 = x

m-3 = multiple of 5

I tried a couple of methods from this point but I can't figure it out. I realize that you can set m to a number such as 8 and get the answer that way but I need the algebraic solution.

 

[stapel]

If m has a remainder of 3 when divided by 5, then:

. . . . .m = 5n + 3

...by nature of division and remainders. Multiplying through by 20, we get:

. . . . .20m = 100n + 60

Dividing by 25, we get:

. . . . .(20m)/25 = (100n + 60)/25

But:

. . . . .100n + 60 = 25(4n) + 25(2) + 10

...so:

. . . . .(100n + 60) = [25(4n) + 25(2) + 10] / 25

In other words, the remainder would be...?

Eliz.

 

[dagr8est]

Wow, okay I see.

 

[Denis]

"When the positive number m is dividied by 5, the remainder is 3.
What is the remainder when 20m is divided by 25?"

From the "nature" of the question, simply pick m=8;
8 / 5 = 1 r 3
8*20 = 160; 160/25 = 6 r 10

By "nature" I mean m can be any number of form 5k + 3.