MathDB

Each day John's mother sends him to the store with

\$1

to buy widgets and gadgets, each of which cost a whole number of cents. On the first day John comes back with

4

widgets,

5

gadgets, and

35

cents in change. On the second day, John comes back with

5

widgets,

4

gadgets, and

39

cents in change. On the third day, John comes back with only

c

cents in change. He hands his mother the change, telling her that he had tripped coming home and broken all the widgets and gadgets. His mother, thinking for a moment, begins yelling at him for lying, as she noticed that there was no way he could have received exactly

c

cents in change given the price of widgets and gadgets. What is the sum of the digits of the least possible value of

c

<span class='latex-bold'>(A) </span>10\qquad<span class='latex-bold'>(B) </span>13\qquad<span class='latex-bold'>(C) </span>15\qquad<span class='latex-bold'>(D) </span>18\qquad<span class='latex-bold'>(E) </span>\text{impossible to determine}

Problem Statement