Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
1 answer:
Let the tens digit of the original number be represented by x. Let the ones digit be y.
The original number is then 10x + y, and the reversed number is 10y + x.
"Five times the sum of the digits is 13 less than the original number" becomes:
"Four times the sum of its digits is 21 less than the reversed number" becomes:
Work with the first equation until it is simpler:
Do the same thing with the second equation:
Now you have a system of two equations to solve.
To eliminate x, multiply the first equation by 3 and multiply the second equation by 5
Add the two equations.
Aha! The one digit of the original number is 8. To find y, put x = 8 into any equation containing both x and y.
Sweet! The tens digit of the original number is 9. The original number is 98 and the reversed number is 89.
Their difference is 9.
The original number is then 10x + y, and the reversed number is 10y + x.
"Five times the sum of the digits is 13 less than the original number" becomes:
"Four times the sum of its digits is 21 less than the reversed number" becomes:
Work with the first equation until it is simpler:
Do the same thing with the second equation:
Now you have a system of two equations to solve.
To eliminate x, multiply the first equation by 3 and multiply the second equation by 5
Add the two equations.
Aha! The one digit of the original number is 8. To find y, put x = 8 into any equation containing both x and y.
Sweet! The tens digit of the original number is 9. The original number is 98 and the reversed number is 89.
Their difference is 9.
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