Respuesta :
Answer:
2 [tex]\frac{1}{16}[/tex]
Step-by-step explanation:
The question state that; the sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number.
First, we need to interpret and represent this statement mathematically
Let n be the number.
The sum means 'addition'
1/6 of that number is 1/6 of n = 1/6 × n = [tex]\frac{n}{6}[/tex]
2 1/2 of that number is 2 1/2 of n = 2 1/2 × n = 5/2 × n = [tex]\frac{5n}{2}[/tex]
So the question says that, when we add; [tex]\frac{n}{6}[/tex] , [tex]\frac{5n}{2}[/tex] and 7 all together, the value is 12 1/2
That is;
[tex]\frac{n}{6}[/tex] + [tex]\frac{5n}{2}[/tex] + 7 = 12 1/2
[tex]\frac{n}{6}[/tex] + [tex]\frac{5n}{2}[/tex] + 7 = [tex]\frac{25}{2}[/tex] ( changing 12 1/2 to improper fraction will give [tex]\frac{25}{2}[/tex] )
So we can now go ahead and solve for n
[tex]\frac{n}{6}[/tex] + [tex]\frac{5n}{2}[/tex] + 7 = [tex]\frac{25}{2}[/tex]
subtract 7 from both-side of the equation
[tex]\frac{n}{6}[/tex] + [tex]\frac{5n}{2}[/tex] = [tex]\frac{25}{2}[/tex] - 7
[tex]\frac{n + 15n}{6}[/tex] = [tex]\frac{25 -14}{2}[/tex]
[tex]\frac{16n}{6}[/tex] = [tex]\frac{11}{2}[/tex]
[tex]\frac{16n}{6}[/tex] can be reduced to give us [tex]\frac{8n}{3}[/tex]
[tex]\frac{8n}{3}[/tex] = [tex]\frac{11}{2}[/tex]
Cross multiply
8n × 2 = 11× 3
16n = 33
Divide both-side of the equation by 16
[tex]\frac{16n}{16}[/tex] = [tex]\frac{33}{16}[/tex]
(On the left-hand side of the equation, 16 will cancel-out 16 leaving us with just, while on the right-hand side of the equation 33 will be divided by 16)
n = [tex]\frac{33}{16}[/tex] = [tex]2\frac{1}{16}[/tex]
Therefore the number is [tex]2\frac{1}{16}[/tex]
The number is 3/2.
Given
The sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2.
System of equations;
When solving the system, you must consider all of the equations involved and find a solution that satisfies all of the equations.
Let, the number be n.
Here, 1/6 of the number n is;
[tex]\rm = \dfrac{1}{6}\times n= \dfrac{n}{6}[/tex]
And 2 1/2 of the number n is;
[tex]\rm = 2\dfrac{1}{2}\times n\\\\=\dfrac{2\times 2+1}{2}\times n\\\\=\dfrac{4+1}{2}\times n\\\\=\dfrac{5}{2}\times n\\\\=\dfrac{5n}{2}[/tex]
Therefore,
The sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2.
[tex]\rm n+\dfrac{n}{6}+\dfrac{5n}{2}+7=12\dfrac{1}{2}\\\\\dfrac{6n+n+15n+42}{6} = \dfrac{12\times 2+1}{2}\\\\\dfrac{22n+42}{6} = \dfrac{24+1}{2}\\\\\dfrac{22n+42}{6} = \dfrac{25}{2}\\\\2(22n+42)=25\times 6\\\\44n+84=150\\\\44n=150-84\\\\44n=66\\\\n = \dfrac{66}{44}\\\\n=\dfrac{3}{2}[/tex]
Hence, the number is 3/2.
To know more about the equation click the link given below.
https://brainly.com/question/12292915
