Summing columns for each value in a different table

Given tables A and B as shown below:

Table A       Table B
+----+---+    +----+-----+-------+
+ id + c +    + id + Aid + value +
+----+---+    +----+-----+-------+
+  1 + 1 +    +  1 +  1  +    50 +
+----+---+    +----+-----+-------+
+  2 + 0 +    +  2 +  1  +    20 +
+----+---+    +----+-----+-------+
+  3 + 1 +    +  3 +  2  +    75 +
+----+---+    +----+-----+-------+
              +  4 +  3  +    23 +
              +----+-----+-------+
              +  5 +  3  +    17 +
              +----+-----+-------+

How does one get the sum of the column B.value for each value of A.id that meets the condition c=1?

That is, the following:

+----+-------+
+ id + value +
+----+-------+
+  1 +    70 +
+----+-------+
+  3 +    40 +
+----+-------+

I've tried doing SELECT A.id as id, SUM(B.value) as value FROM A INNER JOIN B on B.Aid=A.id WHERE c=1, but that just returns the following:

+----+-------+
+ id + value +
+----+-------+
+  3 +   110 +
+----+-------+