I am helping my daughter and I need help on this question in the number 57,733 contains two sets of digits in which one digit is ten times as great as the other what are the values of the digits in each set help please!!!!
http://www.jiskha.com/display.cgi?id=1392477199#1392477199.1392477396
To find the values of the digits in each set, we can break down the number 57,733 and examine its individual digits.
Step 1: Analyze the number
The number 57,733 has five digits. Let's consider the three digits in the middle (the hundreds, tens, and units digits) as one set, and the two digits on the left (the ten thousands and thousands digits) as the other set.
Step 2: Express the digits in terms of variables
Let's assign variables to the digits in each set. For the three-digit set, let's use variables a, b, and c. For the two-digit set, let's use variables x and y.
So, we have:
57,733 = 10,000x + 1,000y + 100a + 10b + c
Step 3: Set up the given condition
According to the problem, one digit must be ten times as great as the other. Let's set up the equation using this condition.
We can express this condition as: a = 10c OR c = 0.1a
Step 4: Substitute the variables
Substitute either a = 10c or c = 0.1a into the original expression for the number: 57,733 = 10,000x + 1,000y + 100a + 10b + c
Step 5: Solve for the variables
Using the given equation, we have two cases to consider:
Case 1: a = 10c
Substituting this into the expression for the number, we have:
57,733 = 10,000x + 1,000y + 100(10c) + 10b + c
Case 2: c = 0.1a
Substituting this into the expression for the number, we have:
57,733 = 10,000x + 1,000y + 100a + 10b + 0.1a
Simplify both equations and solve for the variables to find the values.