Kia112302
Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Five times the sum of the digits of a two-digit number is 13 less than the original number. If you reverse the digits in the two-digit number, four times the sum of its two digits is 21 less than the reversed two-digit number.


(Hint: You can use variables to represent the digits of a number. If a two-digit number has the digit x in tens place and y in one’s place, the number will be 10x + y. Reversing the order of the digits will change their place value and the reversed number will 10y + x.)


The difference of the original two-digit number and the number with reversed digits is........

.

Sagot :

Answer:

The difference of the original two-digit number and the number with reversed digits is 18.

Step-by-step explanation:

Since it's a two digit number, let x represent the tens digit and let y represent the units digit.

Thus, the original two digit number is;

10x + y.

The reverse two digit number is;

10y + x.

We are told that five times the sum of the digits of the two-digit number is 13 less than the original number.

Thus;

5(x + y) = (10x + y) - 13

Multiplying out the bracket gives;

5x + 5y = 10x + y - 13

Rearranging gives;

10x - 5x + y - 5y = 13

5x - 4y = 13 - - - - (3)

Also,we are told that, four times the sum of its two digits is 21 less than the reversed two-digit number. Thus;

4(x + y) = (10y + x) - 21 - - - (4)

Simplifying gives;

4x + 4y = 10y + x - 21

>> 10y - 4y - 4x + x = 21

>> 6y - 3x = 21 - - - (4)

Solving eq(3) and (4) simultaneously gives;

x = 5 and y = 3

Thus,

Original number = 53

Reversed number = 35

Difference between original and reversed number = 53 - 35 = 18

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.