Set up and solve each equation In a magic square each row co

Set up and solve each equation. In a magic square, each row, column, and diagonal has the same sum. Magic sum is

Solution

the given

3x-5 = 2(2x+5)

That is 3x-5 = 4x+10

            -5-10 = 4x - 3x

           -15 = x

Value of x = -15

10x+8 = 12x-18

That is

8 + 18 = 12x – 10x

26 = 2 x

Value of x = 13

4(x-7)= 2x-6

That is 4x-28 = 2x – 6

            4x-2x = 28 – 6

                 2 x = 22

Value of x= 11  

3(y+4) = 5y+30

That is 3y+12 = 5y+30

         12- 30 =5y - 3y

     That is 2y = -18

Value of y = -9

3(2y+4) = 4(y+7)-2

That is

        6y + 12 = 4y +28 -2

        6y - 4y = 28 -2 -12

        2y = 14

Value of y = 7

6y= 10 - 4y

That is 6y+4y = 10

           10 y =10

Value of y = 1

27 - 6x = 3x

That is 27 = 3x+ 6x

                27 = 9x

Value of x= 3

7y+3 = 12y- 2

That is

3 + 2 = 12y – 7y

5= 5 y

Value of y = 1

2y + 2= 3y+3

That is

2- 3= 3y – 2y

Value of y = - 1

8x - (6x - 4) = 10

That is 2x – 4 =10

             2x = 10+ 4 = 14

2x = 14

Value of X=7

6y= 10+4y

That is 2y = 10

Value of y = 5

6(x+7) =2(x+7)

That is 6x + 42 = 2x + 14

             6x – 2x = 14 -42

            4x = - 28

Value of x = -7

Two consecutive whole numbers total 17. Find the larger.

8 and 9 are two consecutive whole numbers

8 + 9 =17

Larger number is 9

Two consecutive odd numbers total 20.

Find the smaller.

9 and 11 are two consecutive odd numbers

9 + 11 = 20

Small number is 9

One number is 4 less than 3 times another. Their sum is 16. Find the smaller.

Let the two numbers are x and y

X = 3y – 4   ---- (1)

X + y = 16 ------( 2 )

From (2)

X = 16 – y ----- (3)

From (1) and (3)

16 – y = 3y – 4

16 + 4 = 3Y + Y

20 = 4 Y

Y =5

Substitute y value in (1)

We get x = 3(5)-4

              X = 11

We get X = 11 and y = 5

The smaller is 5

Two consecutive odd numbers total 32. Find the smaller.

15 and 17 are two consecutive odd numbers.

15 + 17 = 32

Small number is 15.

The magic box is

Row Sum

- 15

13

11

-9

0

7

1

3

1

12

- 1

7

5

-7

4

9

9

5

15

38

Column Sum

0

30

24

0

54

Sum of row sum and column sum

Magic sum is 54

3x-5 = 2(2x+5) That is 3x-5 = 4x+10             -5-10 = 4x - 3x            -15 = x Value of x = -15	10x+8 = 12x-18 That is 8 + 18 = 12x – 10x 26 = 2 x Value of x = 13	4(x-7)= 2x-6 That is 4x-28 = 2x – 6             4x-2x = 28 – 6                  2 x = 22 Value of x= 11	3(y+4) = 5y+30 That is 3y+12 = 5y+30          12- 30 =5y - 3y      That is 2y = -18 Value of y = -9
3(2y+4) = 4(y+7)-2 That is         6y + 12 = 4y +28 -2         6y - 4y = 28 -2 -12         2y = 14 Value of y = 7	6y= 10 - 4y That is 6y+4y = 10            10 y =10 Value of y = 1	27 - 6x = 3x That is 27 = 3x+ 6x                 27 = 9x Value of x= 3	7y+3 = 12y- 2 That is 3 + 2 = 12y – 7y 5= 5 y Value of y = 1
2y + 2= 3y+3 That is 2- 3= 3y – 2y 1 = y Value of y = - 1	8x - (6x - 4) = 10 That is 2x – 4 =10              2x = 10+ 4 = 14 2x = 14 Value of X=7	6y= 10+4y That is 2y = 10 Value of y = 5	6(x+7) =2(x+7) That is 6x + 42 = 2x + 14              6x – 2x = 14 -42             4x = - 28 Value of x = -7
Two consecutive whole numbers total 17. Find the larger. 8 and 9 are two consecutive whole numbers 8 + 9 =17 Larger number is 9	Two consecutive odd numbers total 20. Find the smaller. 9 and 11 are two consecutive odd numbers 9 + 11 = 20 Small number is 9	One number is 4 less than 3 times another. Their sum is 16. Find the smaller. Let the two numbers are x and y X = 3y – 4   ---- (1) X + y = 16 ------( 2 ) From (2) X = 16 – y ----- (3) From (1) and (3) 16 – y = 3y – 4 16 + 4 = 3Y + Y 20 = 4 Y Y =5 Substitute y value in (1) We get x = 3(5)-4               X = 11 We get X = 11 and y = 5 The smaller is 5	Two consecutive odd numbers total 32. Find the smaller. 15 and 17 are two consecutive odd numbers. 15 + 17 = 32 Small number is 15.