Question

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.

Answer 1

Answer:

2 $\frac{1}{16}$

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  = $\frac{n}{6}$

2 1/2 of that number is 2 1/2 of n = 2 1/2 × n  = 5/2 × n = $\frac{5n}{2}$

So the question says that, when we add; $\frac{n}{6}$ ,  $\frac{5n}{2}$  and 7 all together, the value is 12 1/2

That is;

$\frac{n}{6}$  + $\frac{5n}{2}$ + 7 = 12 1/2

$\frac{n}{6}$  + $\frac{5n}{2}$ + 7  = $\frac{25}{2}$         ( changing 12 1/2 to improper fraction will give  $\frac{25}{2}$ )

So we can now go ahead and solve for n

$\frac{n}{6}$  + $\frac{5n}{2}$ + 7  = $\frac{25}{2}$  

subtract 7 from both-side of the equation

$\frac{n}{6}$  + $\frac{5n}{2}$   =  $\frac{25}{2}$   -   7

$\frac{n + 15n}{6}$  =   $\frac{25 -14}{2}$

$\frac{16n}{6}$      =    $\frac{11}{2}$

$\frac{16n}{6}$  can be reduced to give us $\frac{8n}{3}$

$\frac{8n}{3}$   =   $\frac{11}{2}$

Cross multiply

8n × 2  = 11× 3

16n = 33

Divide both-side of the equation by 16

$\frac{16n}{16}$    =   $\frac{33}{16}$

(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 =  $\frac{33}{16}$     = $2\frac{1}{16}$

Therefore the number is  $2\frac{1}{16}$