28.10.2022

A first number plus twice a second number is 10. Twice the first number plus the second totals 32. Find the numbers.

. 5

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Mathematics
Step-by-step answer
P Answered by PhD
42 and -16

Step-by-step explanation:

m,\ n-the\ numbers\\\\\text{The equations:}\\\\(1)\qquad n+2m=10\\(2)\qquad n+m=26\\\\\text{subtract both sides of the equations}\\\\(n+2m)-(n+m)=10-26\\\\n+2m-n-m=-16\qquad\text{combine like terms}\\\\(n-n)+(2m-m)+-16\\\\\boxed{m=-16}\\\\\text{Put the value of m to (2)}:\\\\n+(-16)=26\\\\n-16=26\qquad\text{add 16 to both sides}\\\\\boxed{n=42}

Mathematics
Step-by-step answer
P Answered by PhD

x = 6, y = -2

Step-by-step explanation:

Let the numbers be x and y.

x + 2y = 2

x = 2 - 2y --(1)

2x + y = 10 --(2)

sub (1) into (2):

2(2 - 2y) + y = 10

4 - 3y = 10

y = -2

when y = -2, x = 6

This is a question on simultaneous equations. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)

Mathematics
Step-by-step answer
P Answered by PhD

6 and 2

Step-by-step explanation:

Let the first number =a

Let the second number =b

A first number plus twice a second number is 14.

a+2b=14

Twice the first number plus the second totals 10.

2a+b=10

We solve the two equations simultaneously

a+2b=14 \implies a=14-2b\\$Substitute into the second equation$\\2(14-2b)+b=10\\28-4b+b=10\\-3b=10-28\\-3b=-18\\b=6

Recall:

a=14-2b

=14-2(6)

=14-12

a=2

The two numbers are 6 and 2.

Mathematics
Step-by-step answer
P Answered by Master

1.  This is a like term

24 = 24

2. This is not a like term

12x - 6 = 46

3. This is not a like term

33 = 5x + 43

4.This is a like term

1 = 1

5. This is not a like term

7x = -48

6. This is a like term

25 = 25

7. This is a like term

60 = 60

8. This is a like term

47 = 47

9.This is a like term

20.6 = 20.6

10.This is a like term

10 = 10

Step-by-step explanation:

1. 5x + 4x − 6x = 24

5x + 4x = 9x

9x - 6x = 24

3x = 24

We can replace x and turn it into an 8.

3(8) = 24

3 x 8 = 24

24 = 24

This is a like term.

2. 8x + 5 − 4x + 1 = 46

8x + 4x - 5 + 1 = 46

8x + 4x = 12x

12x - 5 + 1 = 46

5 + 1 = 6

12x - 6 = 46

We cannot replace the x with any number to get 46.

So this is not a like term.

3. 33 = 5(x + 8) + 3

5xX= 5x

5 x 8 = 40

33 = 5x + 40 + 3

40 + 3 = 43

33 = 5x + 43

We cannot replace any number with x and get 33.

This is not a like term.

4. 2x + 3(x − 8) = 1

3 x X = 3x

3 x 8 = 24

2x + 3x - 24 = 1

2x + 3x = 5x

5x - 24 = 1

We can replace the x with 5.

5(5) - 24 = 1

5 x 5 = 25

25 - 24 = 1

1 = 1

This is a like term

5. x + x − 2x + 4x = −48

x + x = 1x because x is always a 1

1x - 2x +4x  = -48

1x + 2x = 3x

4x + 3x = 7x

7x = -48

We cannot replace x with any number.

This is not a like term.

6. 2(x + 5) + 3x = 25

2 x X = 2x

2 x 5 = 10

2x + 10 + 3x = 25

2x + 3x + 10 = 25

2x + 3x = 5x

5x + 10 = 25

We can replace the x with a 3.

5(3) + 10 = 25

5 x 3 = 15

15 + 10 = 25

25 = 25

This is a like term.

7. 60 = 4(x + 3) + 2(x − 3)

4 x X = 4x

4 x 3 = 12

60 = 4x + 12 + 2(x - 3)

2 x X = 2x

2 x 3 = 6

60 = 4x + 12 + 2x - 6

60 = 4x +2x +12 - 6

4x - 2x = 2x

60 = 2x + 12 - 6

12 - 6 = 6

60 = 2x + 6

We can replace the x with a 33.

60 = 2(33) - 6

2 x 33 = 66

66 - 6 = 60

60 = 60

This is a like term.

8. 47 = 2(x + 3) + 3(x − 3)

2 x X = 2x

2 x 3 = 6

47 = 2x + 6 + 3(x - 3)

3 x X = 3x

3 x 3 = 9

47 = 2x + 6 + 3x - 9

47 = 2x + 3x + 6 - 9

2x + 3x =  5x

47 = 5x + 6 - 9

6 - 9 = -3

47 = 5x + -3

We can replace the x with a 10.

47 = 5(10) + -3

5 x 10 = 50

47 = 50 + -3

50 + -3 = 47

47 = 47

This is a like term.

9. −2(x + 1.4) − 1.8 = 20.6

-2 x X = -2x

-2 x 1.4 = -2.8

-2x + -2.8 - 1.8 = 20.6

-2.8 - 1.8 = -4.6

-2x + -4.6 = 20.6

We can replace x with a 8.

-2(8) + -4.6 = 20.6

-2 x 8 = -16

-16 + -4.6 = 20.6

20.6 = 20.6

This is a like term.

10. 8 − 2(x + 4) = 10

2 x X = 2x

2 x 4 = 8

8 - 2x + 8 = 10

8 - 8 + 2x = 10

8 - 8 = 0

0 + 2x = 10

We can replace x with 5.

0 + 2(5) = 10

2 x 5 = 10

0 + 10 = 10

10 = 10

This is a like term.

I hope this helped. I am sorry if you get this wrong. Have a wonderful day.

Mathematics
Step-by-step answer
P Answered by Master

1.  This is a like term

24 = 24

2. This is not a like term

12x - 6 = 46

3. This is not a like term

33 = 5x + 43

4.This is a like term

1 = 1

5. This is not a like term

7x = -48

6. This is a like term

25 = 25

7. This is a like term

60 = 60

8. This is a like term

47 = 47

9.This is a like term

20.6 = 20.6

10.This is a like term

10 = 10

Step-by-step explanation:

1. 5x + 4x − 6x = 24

5x + 4x = 9x

9x - 6x = 24

3x = 24

We can replace x and turn it into an 8.

3(8) = 24

3 x 8 = 24

24 = 24

This is a like term.

2. 8x + 5 − 4x + 1 = 46

8x + 4x - 5 + 1 = 46

8x + 4x = 12x

12x - 5 + 1 = 46

5 + 1 = 6

12x - 6 = 46

We cannot replace the x with any number to get 46.

So this is not a like term.

3. 33 = 5(x + 8) + 3

5xX= 5x

5 x 8 = 40

33 = 5x + 40 + 3

40 + 3 = 43

33 = 5x + 43

We cannot replace any number with x and get 33.

This is not a like term.

4. 2x + 3(x − 8) = 1

3 x X = 3x

3 x 8 = 24

2x + 3x - 24 = 1

2x + 3x = 5x

5x - 24 = 1

We can replace the x with 5.

5(5) - 24 = 1

5 x 5 = 25

25 - 24 = 1

1 = 1

This is a like term

5. x + x − 2x + 4x = −48

x + x = 1x because x is always a 1

1x - 2x +4x  = -48

1x + 2x = 3x

4x + 3x = 7x

7x = -48

We cannot replace x with any number.

This is not a like term.

6. 2(x + 5) + 3x = 25

2 x X = 2x

2 x 5 = 10

2x + 10 + 3x = 25

2x + 3x + 10 = 25

2x + 3x = 5x

5x + 10 = 25

We can replace the x with a 3.

5(3) + 10 = 25

5 x 3 = 15

15 + 10 = 25

25 = 25

This is a like term.

7. 60 = 4(x + 3) + 2(x − 3)

4 x X = 4x

4 x 3 = 12

60 = 4x + 12 + 2(x - 3)

2 x X = 2x

2 x 3 = 6

60 = 4x + 12 + 2x - 6

60 = 4x +2x +12 - 6

4x - 2x = 2x

60 = 2x + 12 - 6

12 - 6 = 6

60 = 2x + 6

We can replace the x with a 33.

60 = 2(33) - 6

2 x 33 = 66

66 - 6 = 60

60 = 60

This is a like term.

8. 47 = 2(x + 3) + 3(x − 3)

2 x X = 2x

2 x 3 = 6

47 = 2x + 6 + 3(x - 3)

3 x X = 3x

3 x 3 = 9

47 = 2x + 6 + 3x - 9

47 = 2x + 3x + 6 - 9

2x + 3x =  5x

47 = 5x + 6 - 9

6 - 9 = -3

47 = 5x + -3

We can replace the x with a 10.

47 = 5(10) + -3

5 x 10 = 50

47 = 50 + -3

50 + -3 = 47

47 = 47

This is a like term.

9. −2(x + 1.4) − 1.8 = 20.6

-2 x X = -2x

-2 x 1.4 = -2.8

-2x + -2.8 - 1.8 = 20.6

-2.8 - 1.8 = -4.6

-2x + -4.6 = 20.6

We can replace x with a 8.

-2(8) + -4.6 = 20.6

-2 x 8 = -16

-16 + -4.6 = 20.6

20.6 = 20.6

This is a like term.

10. 8 − 2(x + 4) = 10

2 x X = 2x

2 x 4 = 8

8 - 2x + 8 = 10

8 - 8 + 2x = 10

8 - 8 = 0

0 + 2x = 10

We can replace x with 5.

0 + 2(5) = 10

2 x 5 = 10

0 + 10 = 10

10 = 10

This is a like term.

I hope this helped. I am sorry if you get this wrong. Have a wonderful day.

Mathematics
Step-by-step answer
P Answered by PhD

x =\frac{14}{3} , y = \frac{25}{3} and z = -3

The numbers are    -3 ,\frac{14}{3} ,  \frac{25}{3}

Step-by-step explanation:

Step(i):-

Given sum of the three numbers is 10

Let x , y , z be the three numbers is 10

x +y + z = 10  ...(i)

Given two times the second number minus the first number is equal to 12

2 × y - x = 12 ...(ii)

Given the first number minus the second number plus twice the third number equals 7

x + y + 2 z = 7 ...(iii)

Step(ii):-

Solving (i) and (iii) equations

                       x + y +   z     =    10  ...(i)

                       x + y + 2 z   =     7 ..   (iii)

                     -      -     -         -              

                     0    0    -z      =   3              

Now we know that    z = -3 ...(a)

from (ii)  equation

           2 × y - x = 12 ...(ii)

               x = 2 y -12  ...(b)

Step(iii):-

substitute equations (a) and (b) in equation (i)

                x+y+z =10

           2 y - 12 + y -3 =10

              3 y -15 =10

              3 y = 10 +15

              3 y =25

               y = \frac{25}{3}

Substitute   y = \frac{25}{3}  and   z = -3 in equation(i) we will get

        x+y+z =10

       x + \frac{25}{3} -3 = 10

       x +\frac{25-9}{3}  = 10

      x +\frac{16}{3}  = 10

      x   = 10 - \frac{16}{3}

     x   =  \frac{30 -16}{3} = \frac{14}{3}

Final answer :-

x =\frac{14}{3} , y = \frac{25}{3} and z = -3

The numbers are  -3 ,\frac{14}{3} ,  \frac{25}{3}

       

Mathematics
Step-by-step answer
P Answered by PhD

The answer to your question is x = -2, y = 5 and z = 7

Step-by-step explanation:

Data

first number = x

second number = y

third number = z

Process

1.- Write equations to solve this problem

                 x + y + z = 10           Equation l

                 2y - x = 12                Equation ll

                  x - y + 2z = 7           Equation lll

2.- Solve equation ll for x

                x = 2y - 12

3.- Substitute the previous equation in equation l and lll

               (2y - 12) + y + z = 10                     (2y - 12) - y + 2z = 7

                2y - 12 + y + z = 10                       2y - 12 - y + 2z = 7

                3y + z = 10 + 12                             y + 2z = 19

                3y + z = 22

4.- Solve for y and z

                     -2(3y + z = 22)

                          y + 2z = 19

                    -6y - 2z = -44

                       y + 2z = 19

                   -5y   + 0 = -25

                      y = -25/-5

                      y = 5

-Find z

                       5 + 2z = 19

                             2z = 19 - 5

                             2z = 14

                               z = 14/2

                               z = 7

5.- Find x

                  x + 5 + 7 = 10

                  x = 10 - 5 - 7

                 x = -2

Mathematics
Step-by-step answer
P Answered by Master
let a=1st number
let b=2nd number
let c=3rd number
then
a+b+c=10
2b-a=12
a-b+2c=7

a+b+c=10
-a+b=12
add
3b+c=22

-a+2b=12
a-b+2c=7
add

b+2c=19

3b+c=22
b+2c=19

3b+c=22
3b+6c=57
subtract
-5c=-35
c=7
b=-2c+19=5
a=2b-12=-2

a=1 number=-2
b=2nd number=5
c=3rd number=7 
Mathematics
Step-by-step answer
P Answered by PhD
The two numbers are 23 and 16 and the method is shown algebraically using simultaneous equations in the photo
The sum of two numbers is 39, twice the first number plus three times the second number is 101 find

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