The number 57,733 contains two sets of digits in such digit is ten times as great as the other.What are the values of the digits in each set.
33 = 3 tens and 3 ones
77 = 7 thousands and 7 hundreds
7725
Let's denote the two sets of digits in the number 57,733 as A and B.
Now, let's assume that the digits in set A are larger than those in set B. So, we have two cases:
Case 1:
Let the digits in set A be x and the digits in set B be y. According to the given information, we can write the following equation:
10x + y = 57,733
Case 2:
Let the digits in set A be y and the digits in set B be x. In this case, we need to reverse the digits. Therefore, the equation becomes:
10y + x = 57,733
To find the values of x and y, we can solve these equations simultaneously.
Now, let's solve Case 1:
10x + y = 57,733
We know that x is ten times greater than y, so we can write:
x = 10y
Substituting this into the equation, we get:
10(10y) + y = 57,733
100y + y = 57,733
101y = 57,733
y = 57,733 / 101
y ≈ 570.63
Since y must be a whole number, we can round y to the nearest whole number, which is 571.
Substituting this back into x = 10y, we find:
x ≈ 10 * 571 = 5710
So, the values of the digits in each set (Case 1) are:
Set A: 5710
Set B: 571
Now, let's solve Case 2:
10y + x = 57,733
We know that x is ten times greater than y, so we can write:
x = 10y
Substituting this into the equation, we get:
10y + 10y = 57,733
20y = 57,733
y = 57,733 / 20
y ≈ 2886.65
Since y must be a whole number, we can round y to the nearest whole number, which is 2887.
Substituting this back into x = 10y, we find:
x ≈ 10 * 2887 = 28,870
So, the values of the digits in each set (Case 2) are:
Set A: 28,870
Set B: 2887
Therefore, depending on the case, the values of the digits in each set are either:
Case 1:
Set A: 5710
Set B: 571
OR
Case 2:
Set A: 28,870
Set B: 2887
To find the values of the digits in each set, we will use a systematic approach.
First, we need to determine the largest digit values since one set of digits is ten times as great as the other. Let's assume the larger set of digits is represented by the variable "x" and the smaller set of digits is represented by the variable "y".
Now, let's break down the number 57,733:
The digit 7 appears twice in the number. We can assume that one of the 7's represents the digit "x" and the other represents the digit "y".
So, the equation becomes:
7x + 7y = 57,733
Next, we extract the number from the equation:
7(x + y) = 57,733
x + y = 57,733 / 7
x + y = 8,247
Now, we know that "x" is ten times greater than "y," so we can set up the second equation:
x = 10y
Substituting the value of "x" in terms of "y" into the equation x + y = 8,247, we get:
10y + y = 8,247
11y = 8,247
y = 8,247 / 11
y = 749
Now, substituting the value of "y" back into the equation x = 10y, we can find "x":
x = 10 * 749
x = 7,490
Therefore, the values of the digits in each set are:
Set 1: 7,490
Set 2: 749