OpenStudy (anonymous):

the sum of 2 number us 44and if the larger number is divided by the samller number then the quotient is 5and smaller # is 2 find the numbers

7 years ago
OpenStudy (shadowfiend):

Ok, so we are told a few things. First off, we'll call the two numbers we're looking at \(x\) and \(y\) -- let's say \(x\) is the smaller number. We are told the sum of the two numbers is 44, so that means: $$ x + y = 44 $$ We are also told that the larger number divided by the smaller number is 5, which means: $$ \frac{y}{x} = 5 $$ Since we said x is the smaller number.

7 years ago
OpenStudy (shadowfiend):

Hm. You said the smaller number is 2?

7 years ago
OpenStudy (anonymous):

the remainder is 2

7 years ago
OpenStudy (shadowfiend):

Ah, ok, so y / x is 5 remainder 2. That means that: $$ 5x + 2 = y $$ Then, we can plug that back into the first equation to get: \[ \begin{valign} x + 5x + 2 &= 44 6x + 2 &= 44 \end{valign} \] Then you can solve that equation to find x, and then you can plug back into \(\frac{y}{x} = 5\) to solve for y. Is that enough for you to get the answer?

7 years ago
OpenStudy (shadowfiend):

Bah, sorry. That was: \[\begin{align} x + 5x + 2 &= 44\\ 6x + 2 &= 44 \end{align}\]

7 years ago
OpenStudy (anonymous):

thnkyou so much :)

7 years ago
OpenStudy (shadowfiend):

No problem, glad to help!

7 years ago