Answer:
a=192
b=96
c=64
d=48
Step-by-step explanation:
So we have [tex]a+b+c+d=400[/tex] where [tex]a,b,c,[/tex] and [tex]d[/tex] are integers.
We also have [tex]a=2b[/tex]and [tex]a=3c[/tex]and [tex]a=4d.[/tex]
[tex]a=2b[/tex] means [tex]a/2=b[/tex]
[tex]a=3c[/tex] means [tex]a/3=c[/tex]
[tex]a=4d[/tex] means [tex]a/4=d[/tex]
Let's plug those in:
[tex]a+b+c+d=400[/tex]
[tex]a+\frac{a}{2}+\frac{a}{3}+\frac{a}{4}=400[/tex]
Multiply both sides by 4(3)=12 to clear the fractions:
[tex]12a+6a+4a+3a=4800[/tex]
Combine like terms:
[tex]25a=4800[/tex]
Divide both sides by 25:
[tex]a=\frac{4800}{25}[/tex]
Simplify:
[tex]a=192[/tex].
Let's go back and find [tex]b,c,d[/tex] now.
b is half of a so half of 192 is 96 which means b=96
c is a third of a so a third of 192 is 64 which means c=64
d is a fourth of a so a fourth of 192 is 48 which means d=48
So
a=192
b=96
c=64
d=48
