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 [tex]x+2.4[/tex].
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:
[tex]15x=12y...(1)[/tex]
[tex]15x=10(x+2.4)...(2)[/tex]
Upon solving 2nd equation, we will get:
[tex]15x=10x+24[/tex]
[tex]15x-10x=10x-10x+24[/tex]
[tex]5x=24[/tex]
[tex]x=\frac{24}{5}[/tex]
[tex]x=4.8[/tex]
Therefore, the smallest number is 4.8.
The biggest number would be [tex]x+2.4\Rightarrow 4.8+2.4=7.2[/tex].
Upon substituting [tex]x=4.8[/tex] in equation (1), we will get:
[tex]15(4.8)=12y[/tex]
[tex]72=12y[/tex]
[tex]y=\frac{72}{12}[/tex]
[tex]y=6[/tex]
Therefore, 2nd number would be 6.
Let us find sum of all numbers as:
[tex]4.8+6+7.2=18[/tex]
Therefore, the sum of all 3 numbers would be 18.
