Answer:
The numbers are 16,24 and 32
Step-by-step explanation:
The question in English is
The arithmetic mean of 3 numbers is 24. The second number is 50% greater than the first and the third is one third greater than the second. What are the numbers?
Let
x---> the first number
y ---> the second number
z ---> the third number
we know that
The arithmetic mean of 3 numbers is 24
so
[tex]\frac{x+y+z}{3}=24[/tex]
[tex]x+y+z=72[/tex] ----> equation A
The second number is 50% higher than the first
Remember that
[tex]100\%+50\%=150\%=150/100=1.50[/tex]
so
[tex]y=1.5x[/tex]
[tex]x=\frac{2}{3}y[/tex] ----> equation B
The third number is is one third greater than the second
Remember that
[tex]1+\frac{1}{3}=\frac{4}{3}[/tex]
so
[tex]z=\frac{4}{3}y[/tex] ----> equation C
substitute equation B and equation C in equation A
[tex]\frac{2}{3}y+y+\frac{4}{3}y=72[/tex]
solve for y
[tex]3y=72\\y=24[/tex]
Find the value of x
[tex]x=\frac{2}{3}(24)=16[/tex]
Find the value of z
[tex]z=\frac{4}{3}(24)=32[/tex]
therefore
The numbers are
16,24 and 32
