Find four integers whose sum is 400 such that the first integer is equal to twice the second integer, three times the third integer and four time the fourth integer.

a=192

b=96

c=64

d=48

Step-by-step explanation:

So we have where and are integers.

We also have and and

means

means

means

Let's plug those in:

Multiply both sides by 4(3)=12 to clear the fractions:

Combine like terms:

Divide both sides by 25:

Simplify:

.

Let's go back and find 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