I lost my coins! This morning I had 7 coins worth 53 cents. How many nickels (5 cent pieces) did I have?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
Immediately we can see that there are three pennies. So now you have 4 coins worth 50 cents. Obviously there are no more pennies. Four dimes is not enough to make 50 cents so there must be at least one quarter. And there can't be two quarters because that would already be 50 cents.
So we have 3 coins worth 25 cents. Quick inspection reveals two dimes and one nickel.
So the answer is (A).
I have an algebraic solution . . . sort of.
Let: .This morning I had 7 coins worth 53 cents.
How many nickels (5 cent pieces) did I have?
We see that
Subtract  - : .
We see that: . , and we know that: .
. . If . . . no
. . Hence: . . . . and
You had one nickel . . . answer (A).