The sum of the digits of a two-figured number is 9. If the digits are interchanged, the number obtained is only 3/8 as large as the original number. Find the number
the answer is 72
To solve this problem, we can represent the two-figured number as follows:
Let the original number be represented as 10x + y, where x represents the tens digit and y represents the units digit.
We are given two conditions:
1. The sum of the digits is 9: x + y = 9
2. If the digits are interchanged, the number obtained is only 3/8 as large as the original number: (10y + x) = (3/8)(10x + y)
We need to find the values of x and y that satisfy both conditions.
Now let's solve the equations step by step:
1. x + y = 9
Rearranging, we get: x = 9 - y (equation 1)
2. (10y + x) = (3/8)(10x + y)
Expanding, we get: 10y + x = (30/8)x + (3/8)y
Rearranging, we get: 10y - (3/8)y = (30/8)x - x
80y - 3y = 30x - 8x
77y = 22x
Now, let's substitute the value of x from equation 1 into equation 2:
77y = 22(9-y)
77y = 198 - 22y
99y = 198
y = 198/99
y = 2
Now substitute the value of y into equation 1:
x = 9 - y
x = 9 - 2
x = 7
Therefore, the tens digit (x) is 7 and the units digit (y) is 2. Thus, the two-figured number is 72.