Question

Three numbers are in the ratio $3:5:7$ . If their sum is $840$ , what are the $3$ numbers?

Answer 1

Hint: In this question, we have to find the largest number. So we will first assume a variable and then multiply it with all the three ratios . After that we will add the numbers and their sum is given, so we will form an equation and then simplify it.
We should know that the ratio of two quantities, $a$ and $b$ in the same units, is the fraction $\dfrac{a}{b}$ and we can write it as $a:b$ . The symbol that is used to denote ratio is: “ $(:)$, colon” .

Complete step by step answer:
It is given that three numbers are in the ratio $3:5:7$ .
Let us use the variable which is multiplied by $x$ .
So now the numbers are $3x,5x,7x$ .
We will now add then and form the equation.
According to the question, we can write
 $3x + 5x + 7x = 840$
We will add the similar terms and then simplify it:
 $15x = 840$
It gives us
$x = \dfrac{{840}}{{15}}$
So the value of $x$ is
$x = 56$ .
We will now write the numbers. By putting the value of $x = 56$ , it gives us
$3 \times 56 = 168$
Similarly for $5x$ , we can write
$5 \times 56 = 280$
And the third number i.e. $7x$ is
$7 \times 56 = 392$ .
Therefore there are our required numbers.
Hence the numbers are: $168,280,392$

Note:
We should remember the following points while solving the ratios:
a) The comparison or simplified form of two quantities of the same kind is known as ratio.
b) While comparing two things, the units should be similar.
c) In the ratio $a:b$ , we call $a$ as the first term and the second term is called antecedent or consequent.
d) We can do the comparison of two ratios, if the ratios are equivalent like the fractions.