Amy, Betty, Carmen and Dee spent all their money at the corner store. One girl s

Question

Amy, Betty, Carmen and Dee spent all their money at the corner store. One girl spent her dime on candy; another spent her quarter to buy a ball; a third bought a coloring book for thirty five cents; and the fourth spent forty cents on two comic books. Each paid for her purchase with t he exact change. Upon leaving the store the girls made the following true statements.
Amy said: "if i had a quarter, then so did Betty. Betty had a nickel if and only if Carmen did. If i had a dime, then so did Dee."
Betty said:" If i had a quarter, then so did Amy. if i had a nickel then so did Dee."
Carmen said: " If i had a dime then so did Amy. If Amy did not have a quarter then neither did i.
Dee said: "if I had a quarter,t hen so did Carmen. Betty had a dime. None of us had any pennies."
what did each girl buy?

Explanation / Answer

I started by accepting that Amy had a quarter and that Betty did too. The last statement said that Better also had a dime. That gives her 35 cents and the coloring book. Then lets say that Amy had a dime so that Dee had a dime too. Thus, Dee has the dime and the candy. Then lets give Amy a nickel so she has the 40 cents to get 2 comics (because Betty already had the coloring book for 35 cents). That leaves Carmen with needing a quarter for the ball (because thats the only thing left).

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