QuestionFind a two-digit number where the sum of its digits is 13 and adding 27 reverses its digits. Options: (a) 48 (b) 53 (c) 58 (d) 57 (e) None.

Studdy Solution

STEP 1

Assumptions1. The number is a two-digit number. . The sum of the digits of the number is13.
3. When27 is added to the number, the digits of the number are reversed.

STEP 2

Let's represent the two-digit number as10a + b, where a and b are the tens and units digits respectively.

STEP 3

According to the problem, the sum of the digits a and b is13. We can write this as $a + b =13$

STEP 4

The problem also states that when27 is added to the number, the digits are reversed. This means that the number becomes10b + a. We can write this as $10a + b +27 =10b + a$

STEP 5

Now we have a system of two equations. We can solve this system to find the values of a and b.

STEP 6

First, let's simplify the second equation. We can do this by subtracting a and b from both sides $9a -9b =27$

STEP 7

We can simplify this equation further by dividing both sides by9 $a - b =3$

STEP 8

Now we have a new system of two equations1. $a + b =13$ 2. $a - b =3$

STEP 9

We can solve this system by adding the two equations together. This will eliminate b $2a =16$

STEP 10

Divide both sides by2 to find the value of a $a =8$

STEP 11

Substitute a =8 into the first equation to find the value of b $8 + b =13$

STEP 12

Subtract8 from both sides to find the value of b $b =5$

STEP 13

Now that we have the values of a and b, we can find the original two-digit number. This is given by10a + b $Number =10a + b$

STEP 14

Substitute a =8 and b = into the equation to find the number $Number =10 \\times8 +$

STEP 15

Calculate the number $Number =80 +5 =85$ The number is85, which is not listed in the options. Therefore, the answer is (e) None of these.

Was this helpful?

QuestionFind a two-digit number where the sum of its digits is 13 and adding 27 reverses its digits. Options: (a) 48 (b) 53 (c) 58 (d) 57 (e) None.

Studdy Solution

STEP 1

Assumptions1. The number is a two-digit number. . The sum of the digits of the number is13.
3. When27 is added to the number, the digits of the number are reversed.

STEP 2

Let's represent the two-digit number as10a + b, where a and b are the tens and units digits respectively.

STEP 3

According to the problem, the sum of the digits a and b is13. We can write this as $a + b =13$

STEP 4

The problem also states that when27 is added to the number, the digits are reversed. This means that the number becomes10b + a. We can write this as $10a + b +27 =10b + a$

STEP 5

Now we have a system of two equations. We can solve this system to find the values of a and b.

STEP 6

First, let's simplify the second equation. We can do this by subtracting a and b from both sides $9a -9b =27$

STEP 7

We can simplify this equation further by dividing both sides by9 $a - b =3$

STEP 8

Now we have a new system of two equations1. $a + b =13$ 2. $a - b =3$

STEP 9

We can solve this system by adding the two equations together. This will eliminate b $2a =16$

STEP 10

Divide both sides by2 to find the value of a $a =8$

STEP 11

Substitute a =8 into the first equation to find the value of b $8 + b =13$

STEP 12

Subtract8 from both sides to find the value of b $b =5$

STEP 13

Now that we have the values of a and b, we can find the original two-digit number. This is given by10a + b $Number =10a + b$

STEP 14

Substitute a =8 and b = into the equation to find the number $Number =10 \\times8 +$

STEP 15

Calculate the number $Number =80 +5 =85$ The number is85, which is not listed in the options. Therefore, the answer is (e) None of these.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind a two-digit number where the sum of its digits is 13 and adding 27 reverses its digits. Options: (a) 48 (b) 53 (c) 58 (d) 57 (e) None.

Studdy Solution

STEP 1

Assumptions1. The number is a two-digit number. . The sum of the digits of the number is13.3. When27 is added to the number, the digits of the number are reversed.

STEP 2

Let's represent the two-digit number as10a + b, where a and b are the tens and units digits respectively.

STEP 3

According to the problem, the sum of the digits a and b is13. We can write this asa+b=13a + b =13a+b=13

STEP 4

The problem also states that when27 is added to the number, the digits are reversed. This means that the number becomes10b + a. We can write this as10a+b+27=10b+a10a + b +27 =10b + a10a+b+27=10b+a

STEP 5

Now we have a system of two equations. We can solve this system to find the values of a and b.

STEP 6

First, let's simplify the second equation. We can do this by subtracting a and b from both sides9a−9b=279a -9b =279a−9b=27

STEP 7

We can simplify this equation further by dividing both sides by9a−b=3a - b =3a−b=3

STEP 8

Now we have a new system of two equations1. a+b=13a + b =13a+b=132. a−b=3a - b =3a−b=3

STEP 9

We can solve this system by adding the two equations together. This will eliminate b2a=162a =162a=16

STEP 10

Divide both sides by2 to find the value of aa=8a =8a=8

STEP 11

Substitute a =8 into the first equation to find the value of b8+b=138 + b =138+b=13

STEP 12

Subtract8 from both sides to find the value of bb=5b =5b=5

STEP 13

Now that we have the values of a and b, we can find the original two-digit number. This is given by10a + bNumber=10a+bNumber =10a + bNumber=10a+b

STEP 14

Substitute a =8 and b = into the equation to find the numberNumber=10times8+Number =10 \\times8 +Number=10times8+

STEP 15

Calculate the numberNumber=80+5=85Number =80 +5 =85Number=80+5=85The number is85, which is not listed in the options. Therefore, the answer is (e) None of these.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The number is a two-digit number. . The sum of the digits of the number is13.
3. When27 is added to the number, the digits of the number are reversed.

According to the problem, the sum of the digits a and b is13. We can write this as $a + b =13$

The problem also states that when27 is added to the number, the digits are reversed. This means that the number becomes10b + a. We can write this as $10a + b +27 =10b + a$

First, let's simplify the second equation. We can do this by subtracting a and b from both sides $9a -9b =27$

We can simplify this equation further by dividing both sides by9 $a - b =3$

Now we have a new system of two equations1. $a + b =13$ 2. $a - b =3$

We can solve this system by adding the two equations together. This will eliminate b $2a =16$

Divide both sides by2 to find the value of a $a =8$

Substitute a =8 into the first equation to find the value of b $8 + b =13$

Subtract8 from both sides to find the value of b $b =5$

Now that we have the values of a and b, we can find the original two-digit number. This is given by10a + b $Number =10a + b$

Substitute a =8 and b = into the equation to find the number $Number =10 \\times8 +$

Calculate the number $Number =80 +5 =85$ The number is85, which is not listed in the options. Therefore, the answer is (e) None of these.