C50
Question: A three-digit number has two properties. The tens-digit and the ones-digit add up to 5. If the number is written with the digits in the reverse order, and then subtracted from the original number, the result is 792. Use a system of equations to find all of the three-digit numbers with these properties.
tens-digit and ones-digit add up to 5
let x in tens-digit and y in ones-digit and z in hundereds-digit
so we have 100z + 10x + y and x + y = 5
written with the digits in the reverse order
so we have 100y + 10x + z
subtracted from the original number, the result is 792
then the equation is 100z + 10x + y - (100y + 10x + z) = 792
simplify: 99z - 99y = 792(a)
remember we also have x + y = 5(b). From equation a, we know that we don’t need to pay too much attention in x value. so we are going to exam y value from equation b, because equation b is much simpler than equation a.
- the posible values for y: 0, 1, 2, 3, 4, 5
after calculation:
y = 0: z = 8, x = 5 -> 850
y = 1: z = 9, x = 4 -> 941
y = 2: z = 10, x = 3 -> 1032
y = 3: z = 11, x = 2 -> 1123
y = 4: z = 12, x = 1 -> 1214
y = 5: z = 13, x = 0 -> 1305
since this number only has three digit. The answer will be either 850 or 941.