Answered

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Question 4: 20 pts
The sum of the digits of a two-digit number is 11. When the digits are reversed the new number is
27 more than the original number. Find the original number. Check your answer.

Sagot :

billgkgk

Answer: The numbers are 74 and 47

Step-by-step explanation: X and Y represent the digits. A digit in the Tens place has 10 times its base value. So we can set up equations to model the information given:

10x+y = 10y + x +27

X + Y = 11

y =11-x Rewritten to substitute for y in the first equation.

10x + 11-x = 10(11-x)+x +27 Distribute and then combine like terms.

10x -x +11 = 110 -10x +x

9x + 11 = 110 +27 - 9x Add 9x to both sides and subtract 11 from both sides.

9x +9x = 110 + 27 - 11 Combine like terms:

18x = 126 Divide both sides by 18

x = 7

7 +y= 11 Substitute 7 for x to solve for y.

y= 4

Substitute the values of x and Y into the original equation.

70 +4 = 40 +7 + 27 Combine

The numbers look like 74 and 47.

Check:

74 = 47 + 27 Add 47+27

74 = 74

True!

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