1.The Sum Of Two Numbers Is 29.If The Smaller Is Doubled And The Larger Increased By 7, The Resulting Numbers Will Be Equal. Find The Two Numbers, 2.I

1.the sum of two numbers is 29.if the smaller is doubled and the larger increased by 7, the resulting numbers will be equal. find the two numbers

2.if 2 is added to half of a number, the reult is one more than the original number. What is the original number?

3.the tens digit of a number is three times the ones digit. the sum of the digits in the number is 8. What is the number?

4. The sum of the digits of a two-digit number is 7 . the value of the number is 2 less than 12 times the tens digit. Find the number?

WITH SOLUTION... thank you

 

Answer:

1.  Let x and y be the two numbers

x + y = 29 (Equation 1)

2x = y + 7 (Equation 2)

Find the value of x or y by using Equation 1:

x + y = 29

y = 29 - x

Substitute the value of y to Equation 2:

2x = y + 7

2x = 29 - x + 7

2x + x = 29 + 7

3x = 36

3x/3 = 36/3

x = 12

2x = y + 7

2(12) = y + 7

24 = y + 7

24 - 7 = y

y = 17

2.

0.5x + 2 = x + 1

0.5x - x = 1 - 2

-0.5x = -1

-0.5x/-0.5 = -1/-0.5

x = 2

3. Let y be the tens digit of a number and x be the ones digit:

y = 3x (Equation 1)

x + y = 8 (Equation 2)

Substitute Equation 1 to Equation 2:

x + y = 8

x + (3x) = 8

4x = 8

4x/4 = 8/4

x = 2

Use the value of x to find y:

y = 3x

y = 3(2)

y = 6

The number is 62

4. Let y be the tens digit of a number

Let x be the ones digit

Let 10y + x be the value of the whole number

x + y = 7 (Equation 1)

10y + x = 12y - 2 (Equation 2)

10y - 12y + x = - 2

-2y + x = -2 (Equation 3)

Find the value of x using Equation 1:

x + y = 7

x = 7 - y

Then substitute it to Equation 3:

-2y + x = -2

-2y + (7 - y) = -2

-3y = -2 - 7

-3y/3 = -9/-3

y = 3

Substitute the value of y to get the value of x in Equation 1:

x + y = 7

x + 3 = 7

x = 7 - 3

x = 4

The number is 34.


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