MATH HOMEWORK HELP plzzzzzzzzzz!!!!?

Question

In this addition problem, the letters Y, O , and U represent three different digits. What number does YOU represent?

YOU + YOU + YOU = UUU

Answer 1

You oculd solve this as a system of three equations in three unknowns... are you learning to solve systems?
3(100y + 10o + 1u) = 100u + 10u + u = 111u
300y + 30o + 3u = 111u
300y + 30o = 108u
Divide by 6 to simplify
50y + 5o = 18u
In addition, y, o, and u must all be whole numbers less than or equal to 9
from here we can only do trial and error. Choose a value for u, say 1, see what values of y and o come from it:
50y + 5o = 18
You can see that u would have to be a larger number because otherwise y and or o would be negative.
So let's try u = 9
50y + 5o = 18x9 = 162
Look at the number some more. 50y can be numbers like 50, 100, 150, etc. 5y must end in 5 or 0 That means that 50y + 5o must end in 5 or 0. 18u must also end in 5 or 0. So u must be 5.
Substituting,
50y + 5o = 90
10y + o = 18
Since y and o must be whole single digit numbers, y = 1 and o = 8
185 + 185 + 185 = 555

Answer 2

Remember to think of what each PLACE means -- Y is in the hundreds place so it has a value of 100 times whatever the digit is. O is in the tens place so it has a vlaue of 10 times watever the digfit is. And U is in the ones place so it has a value of just whatever the digit is.

Therefore, the number represented by "YOU" actually has a value of 100*Y + 10*O + U.

Similarly, the number represented by "UUU" has a value of 100*U + 10*U + U, which is a total of 111*U.

Witing this all out then, the addition equation in your question becomes:

(100*Y + 10*O + U) + (100*Y + 10*O + U) + (100*Y + 10*O + U) = 111*U

Adding all those bits together we get:

300*Y + 30*O + 3*U = 111*U

Simplifying by subtracting the term of 3*U form both sides, we get:

300*Y + 30*O = 108*U

which I will just write in the normal algebra way which is:

300Y + 30O = 108U

You can limit the scope of possibilities by looking at it this way:

Allowing Y to be zero, the equation "300Y + 30O = 108U" simplifies to "30O = 108U" and solving for U, we get "U = 30O / 108" -- now checking each possible value of U (which cannot be 0), we find that no value works, so Y cannot be 0.

Similarly, if we allow O to be 0 then the equation "300Y + 30O = 108U" simplifies to "300Y = 108U" and solving for U, we get "U = 300Y / 108" -- now checking each possible value of Y (which cannot be 0 because then O = Y which is not allowed), we again find that no value works. O cannot be 0.

So we know that neither Y, O, nor U can be zero. They each must be 1, 2, 3, 4, 5, 6, 7, 8, or 9.

But we also know that the last digit of 108*U must be zero -- this is because we have proven that "300Y + 30O = 108U" and by definition, no matter what Y and O are, 300Y + 30O will always end in zero (because 300Y must end in 00 and 30O must end in 0, and the sum of whatever these are must end in 0). There are only two digits that meet this requirement, namely 0 and 5:
108*0 = 0
108*5 = 540

U cannot be zero, because then Y and O would both also have to be zero in order for the equation "300Y + 30O = 108U" to be true. This would violate the restriction that the digits are all different.

Therfore, U is 5 and 108*U is 540. SO plug this back into the equation "300Y + 30O = 108U" and we get:
300Y + 30O = 540

Now lets do some factoring to take a factor of 10 out of each side:
10*(30Y+3O) = 10*54
30Y + 3O = 54

Aha! We can do the same trick as before -- "3*O" must end in the digit 4, because "30*Y" ends in 0 and therfore does not affect the ones column of the addition. Which digits when multiplied by 3 end in 4? Only 8 does:
3*8 = 24

So now we know that U = 5 and O = 8! Lets substitute the values back into the original equation:

300Y + 30O = 108U
300Y + 30*8 = 108*5
300Y + 240 = 540
300Y = 540 - 240
300Y = 300
Y = 300 / 300
Y = 1

So now we have our answer:
Y = 1
O = 8
U = 5

YOU = 185

And we can test this out:

185 + 185 + 185 = 555?

Yes it does, so that is our answer.

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But I really like the first part of kpxxbladexx145 's answer, it is a more elegant way of doing what I just did. Simply recognise that UUU will have to be either 111, 222, 333, etc and that the final digit of that number divided by 3 must be the same as the final digit of that number, therfore UUU must be 555 because no other number works -- this shaves a couple steps off my approach.

Answer 3

Try to work this backwards. UUU. That means its a 3 digit number with the numbers being the same. There are only 8 possible differnt UUU's.(999,888,777,etc). Now. Start with 999 and divide by 3 because there are 3 YOU and look for the output. if you were to use 999 then you want the answer to ahve any number for the first to digits not the be the same and the last digit to be 9 i.e. ??9. But its not. You can go down.
but the answer is 555

185+185+185 = 555

Answer 4

B (Base) = 3 H (top) = 4 formula to locate the section for a triangle is B x H = a million/2A So put in the #'s like so.. 3 x 4 = a million/2A So the respond could be a million/2 of 12. So the section could be 6.

Answer 5

185 + 185 + 185 = 555

Answer 6

185

185 + 185 + 185 = 555

=)

Answer 7

U=O
Y= Any positive number
O= The negative opposite
U= 000
Its cheap but it works.

Answer 8

y=any #
o=any #
u=0
you=0