I have three times as many hundreds as I have tens.I have three times tens as I have units.what number am i
Let's assume the number of units is 'x'.
According to the given information, you have three times as many tens as you have units, so the number of tens is 3x.
Also, you have three times as many hundreds as you have tens, so the number of hundreds is 3 * 3x = 9x.
To summarize, the number can be represented as 9x hundreds, 3x tens, and x units.
Since each hundred represents 100, and each ten represents 10, we can express the number as:
9x * 100 + 3x * 10 + x = 900x + 30x + x = 931x
Hence, the number you are referring to is 931x, where x is the number of units.
Let's call the number of hundreds you have "h," the number of tens "t," and the number of units "u."
According to the given information, we can set up the following equations:
1. h = 3t (You have three times as many hundreds as tens.)
2. t = 3u (You have three times as many tens as units.)
We can substitute the value of t from equation 2 into equation 1:
h = 3(3u)
h = 9u
Since the number of units is arbitrary, let's assign a value to it. Let's say u = 1.
Substituting the value of u into equation 2:
t = 3(1)
t = 3
Finally, substituting the values of t and u into equation 1:
h = 3(3)
h = 9
Therefore, the number you are is 9 hundreds, 3 tens, and 1 unit, which forms the number 931.
To solve this problem, let's assign variables to the unknown quantities. Let's use:
x = number of units
y = number of tens
z = number of hundreds
According to the given information:
1. "I have three times as many hundreds as I have tens."
This can be expressed as: z = 3y.
2. "I have three times tens as I have units."
This can be expressed as: y = 3x.
Now, let's substitute the second equation into the first equation:
z = 3(3x)
z = 9x
We also know that the total number is formed by adding the units, tens, and hundreds:
Total number = x + 10y + 100z
Substituting the values of y and z we found earlier:
Total number = x + 10(3x) + 100(9x)
Total number = x + 30x + 900x
Total number = 931x
Since the total number must be a whole number, x must be a multiple of 931. Let's try some values to find the correct number:
x = 1, Total number = 931(1) = 931 (not valid)
x = 2, Total number = 931(2) = 1862 (not valid)
x = 3, Total number = 931(3) = 2793 (not valid)
x = 4, Total number = 931(4) = 3724 (not valid)
x = 5, Total number = 931(5) = 4655 (not valid)
x = 6, Total number = 931(6) = 5586 (not valid)
x = 7, Total number = 931(7) = 6517 (not valid)
x = 8, Total number = 931(8) = 7448 (not valid)
x = 9, Total number = 931(9) = 8379 (not valid)
x = 10, Total number = 931(10) = 9310 (valid)
Therefore, the number you are is 9310.