QuestionFind a two-digit number where the unit's digit is 1 more than the ten's digit and equals 4 times the sum of its digits. Choices: (a) 14 (b) 15 (c) 12 (d) 17 (e) None.

Studdy Solution

STEP 1

Assumptions1. The unit's digit in the two-digit number is greater than the ten's digit by1. . The number equals four times the sum of its digits.

STEP 2

Let's denote the ten's digit as $x$ and the unit's digit as $y$ . According to the problem, we have the following two equations1. $y = x +1$
2. $10x + y =4(x + y)$

STEP 3

Substitute $y = x +1$ into the second equation, we get $10x + x +1 =(x + x +1)$

STEP 4

implify the equation $11x +1 =8x +4$

STEP 5

Subtract $8x$ from both sides of the equation $3x +1 =4$

STEP 6

Subtract1 from both sides of the equation $3x =3$

STEP 7

Divide both sides of the equation by3 $x =1$

STEP 8

Substitute $x =1$ into the first equation $y = x +1$ $y =1 +1 =2$

STEP 9

So the two-digit number is $x + y =* +2 =12$ .
So the number is12. The correct answer is (c)12.

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QuestionFind a two-digit number where the unit's digit is 1 more than the ten's digit and equals 4 times the sum of its digits. Choices: (a) 14 (b) 15 (c) 12 (d) 17 (e) None.

Studdy Solution

STEP 1

Assumptions1. The unit's digit in the two-digit number is greater than the ten's digit by1. . The number equals four times the sum of its digits.

STEP 2

Let's denote the ten's digit as $x$ and the unit's digit as $y$ . According to the problem, we have the following two equations1. $y = x +1$
2. $10x + y =4(x + y)$

STEP 3

Substitute $y = x +1$ into the second equation, we get $10x + x +1 =(x + x +1)$

STEP 4

implify the equation $11x +1 =8x +4$

STEP 5

Subtract $8x$ from both sides of the equation $3x +1 =4$

STEP 6

Subtract1 from both sides of the equation $3x =3$

STEP 7

Divide both sides of the equation by3 $x =1$

STEP 8

Substitute $x =1$ into the first equation $y = x +1$ $y =1 +1 =2$

STEP 9

So the two-digit number is $x + y =* +2 =12$ .
So the number is12. The correct answer is (c)12.

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QuestionFind a two-digit number where the unit's digit is 1 more than the ten's digit and equals 4 times the sum of its digits. Choices: (a) 14 (b) 15 (c) 12 (d) 17 (e) None.

Studdy Solution

STEP 1

Assumptions1. The unit's digit in the two-digit number is greater than the ten's digit by1. . The number equals four times the sum of its digits.

STEP 2

Let's denote the ten's digit as xxx and the unit's digit as yyy. According to the problem, we have the following two equations1. y=x+1y = x +1y=x+12. 10x+y=4(x+y)10x + y =4(x + y)10x+y=4(x+y)

STEP 3

Substitute y=x+1y = x +1y=x+1 into the second equation, we get10x+x+1=(x+x+1)10x + x +1 =(x + x +1)10x+x+1=(x+x+1)

STEP 4

implify the equation11x+1=8x+411x +1 =8x +411x+1=8x+4

STEP 5

Subtract 8x8x8x from both sides of the equation3x+1=43x +1 =43x+1=4

STEP 6

Subtract1 from both sides of the equation3x=33x =33x=3

STEP 7

Divide both sides of the equation by3x=1x =1x=1

STEP 8

Substitute x=1x =1x=1 into the first equation y=x+1y = x +1y=x+1y=1+1=2y =1 +1 =2y=1+1=2

STEP 9

So the two-digit number is x+y=∗+2=12x + y =* +2 =12x+y=∗+2=12.So the number is12. The correct answer is (c)12.

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Let's denote the ten's digit as $x$ and the unit's digit as $y$ . According to the problem, we have the following two equations1. $y = x +1$
2. $10x + y =4(x + y)$

Substitute $y = x +1$ into the second equation, we get $10x + x +1 =(x + x +1)$

implify the equation $11x +1 =8x +4$

Subtract $8x$ from both sides of the equation $3x +1 =4$

Subtract1 from both sides of the equation $3x =3$

Divide both sides of the equation by3 $x =1$

Substitute $x =1$ into the first equation $y = x +1$ $y =1 +1 =2$

So the two-digit number is $x + y =* +2 =12$ .
So the number is12. The correct answer is (c)12.