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The sum of three numbers is 4. The second number is 1 more than twice the first. The sum of the first and third is –1. Find the numbers.

Respuesta :

connorcharonis
1st condition: x + y + z = 4
2nd condition: y = 2x + 1
3rd condition: x + z = - 1 <=> z = - x - 1

Based on the 2nd and 3rd, we replace the 1st as following:

x + 2x + 1 - x - 1 = 4 <=>

2x = 4 <=>

x = 2

Since x = 2, we solve the 2nd as following:

y = 2x + 1 <=>

y = 2*2 + 1 <=>

y = 4 + 1 <=>

y = 5


Same thing for the 3rd:

z = - x - 1 <=>

z = - 2 - 1 <=>

z = - 3
Lanuel

1. The first number is equal to 2.

2. The second number is equal to 5.

3. The third number is equal to -3.

  • Let the first number be a.
  • Let the second number be b.
  • Let the third number be c.

Translating the word sentence into an algebraic expression, we have;

The sum of three numbers is 4:

[tex]a+b+c=4[/tex]   ....equation 1.

The second number is 1 more than twice the first:

[tex]b=2a+1[/tex]    ....equation 2.

The sum of the first and third is –1:

[tex]a+c=-1[/tex]    ....equation 3.

From eqn. 3, we have:

[tex]c=-1-a[/tex]   ....equation 4.

Substituting into eqn. 1, we have:

[tex]a+2a+1+(-1-a)=4\\\\3a+ 1-1-a=4\\\\2a=4\\\\a=\frac{4}{2}[/tex]

a = 2

To find the value of b:

[tex]b=2a+1\\\\b=2(2)+1\\\\b=4+1[/tex]

b = 5

To find the value of c:

[tex]c=-1-a\\\\c=-1-2\\\\[/tex]

c = -3

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