Question

The biggest among three numbers is 2.4 larger than the smallest one. If 15 times the smallest one is equal to 12 times the second and 10 times the third, what is the sum of all three numbers?

Answer 1

Answer:

18

Step-by-step explanation:

Let x represent smallest number and y represent second number.

We have been given that the biggest among three numbers is 2.4 larger than the smallest one. So biggest number would be $x+2.4$.

We are also told that 15 times the smallest one is equal to 12 times the second and 10 times the third. We can represent this information in equations as:

$15x=12y...(1)$

$15x=10(x+2.4)...(2)$

Upon solving 2nd equation, we will get:

$15x=10x+24$

$15x-10x=10x-10x+24$

$5x=24$

$x=\frac{24}{5}$

$x=4.8$

Therefore, the smallest number is 4.8.

The biggest number would be $x+2.4\Rightarrow 4.8+2.4=7.2$.

Upon substituting $x=4.8$ in equation (1), we will get:

$15(4.8)=12y$

$72=12y$

$y=\frac{72}{12}$

$y=6$

Therefore, 2nd number would be 6.

Let us find sum of all numbers as:

$4.8+6+7.2=18$

Therefore, the sum of all 3 numbers would be 18.