There is not enough information to uniquely determine $a,b,c$ and $d$ simply from the equation
$$ 0.4a + 0.3b +0.2c + 0.1d = 74$$
In fact, there are an infinite number of real valued solutions to this equation. Restricting $a,b,c,d \in [0,100]$ removes many possible solutions, but it still not enough. To see this, pick one of the variables and isolate it on the left hand side. I will choose to solve for $a$, but I just as easily could have picked any of the others. Doing this gives:
$$ a = \frac{74-0.3b-0.2c-0.1d}{0.4}=185 - \frac{3}{4}b - \frac{1}{2}c - \frac{1}{4}d$$
Now we have an expression for $a$. But we also want $0 \leq a\leq100$. Substituting the expression we found for $a$, into this inequality gives:
$$ 0\leq 185 - \frac{3}{4}b - \frac{1}{2}c - \frac{1}{4}d\leq100 $$
We can clean this up a little bit by multiplying by $4$, subtracting the constant term, and then multiplying by $-1$:
$$ 0\leq740-3b-2c-d\leq400$$
$$ -740\leq-3b-2c-d\leq-340$$
$$ 340\leq 3b+2c+d\leq740$$
So, any $b,c,d \in [0,100]$ that satisfies this inequality will work for us. Then, once we have $b,c,$ and $d$, we can plug them back into our expression for $a$ and we will have a solution.
It's not hard to find $b,c,$ and $d$ to satisfy the inequality. For example $b=80,c=80,d=80$ works. Plugging these back into the first expression gives $a=65$. Here we have a set of numbers that solve the original problem you posed. It's not hard to see that there are an infinite amount of numbers that will work. Just imagine changing $b,c,$ and $d$ a little bit. If the change is small enough, they will still satisfy the inequality, and you will get another $a$ that works using these new values in the original expression.
