I am just very confused by the wording of this problem the math makes sense after the problem is translated. I don't know how to translate on my own though.

Rebekah, let's help you here. "When the integer n is divided by 2" = n/2;
"the quotient is u, and the remainder is 1" = u + 1/2. Why is "the remainder is 1" translated as 1/2? Because we were dividing the integer by 2, so any remainder must also div by 2, hence 1/2.

Now, translate the next sentence: "when integer n is divided by 5" = n/5; the quotient is v and the remainder is 3" = v + 3/5

So we have two equations:
n/2 = u + 1/2, which can be rewritten after multiplying by 2 as n = 2u + 1
n/5 = v + 3/5, which can be rewritten after multiplying by 5 as n = 5v + 3

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I agree, the wording is confusing. I just look at it like this:

n=[what we don't know, the quotient]*[what it's divided by]+[remainder].

Then set the 2 equations equal to each other and solve. Great luck!

I don't understand how it jumps from a positive addition problem to a subtraction problem. I still don't see why the answer 2u+5v=4 is wrong. Is it some simple rule I'm forgetting?

K Rob,

We know:
n = 2u+1 and n = 5v + 3 from the question, then
2u = n -1 and 5v = n -3, so
2u + 5v = n -1 + n -3 = 2n -4
You cannot get 2u +5v = 4 if n is not 4

How do i get from
' 2u+5v = 2n -4 ' to the answer?
Really confused

Julie, express n using v or u. Then simplify the equation. You will get the right answer.."

What am I doing wrong here:
After translating into math
n/2+u=1
n/2+u=1/2
(x2)= n+2u=1,,,,,,how did u get "n=2u+1"

Hussam, your question has been answered in the thread. Please follow the previous posts by Joel Brainer our contributor.

the answer is right. i just need more details as to how it was transformed into 2u-5v=2. If someone forgets the basics of math, this can be quite confusing.

I'm not sure how 2u + 1 = 5v + 3
Rearranges to 2u - 5v = 2

Sara, that is from basic algebra. You can add or subtract or multiply or divide both sides of an equation, if you use the same number. 2u+1=5v+3; subtract 1 from both sides, then subtract 5v from both sides.

This question looked like that n is the one divided but not the rest, hence it seems to me that, for the jest equation as an example,
n/2=v+1
Because to get the "n" you have to multiply both by 2 so
n=2v+2
It seems weird to get
n/2=v+1/2 because if this is the case v also needs to be divided by 2
n/2=v/2+1/2
I can still tell that this one is obviously wrong understanding from the question. My question is why v is not divided if the reminder is divided by 2.

"the quotient is u, and the remainder is 1" = u + 1/2. Why is "the remainder is 1" translated as 1/2? Because we were dividing the integer by 2, so any remainder must also div by 2, hence 1/2.

But why not dividing u also?

I would like to learn it as dividend= divisor( quotient) + remainder...
M I following correctly?

Please explain this one

It feels like this question can ask for a lot of math if you happen to try the four wrong answers first. Do you have a suggestion for narrowing down the correct answer to fewer choices so we don't waste a lot of time?

Never mind. I see were I misunderstood what this was asking.