Question

Two stockings have different amounts of candy canes. The girl said to the boy, "if I give you one of my candy canes, we'll have an even amount. but if you give me one of yours, I'll have twice as much as you." How many candy canes did they have?

Answer 1

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Answer:

• girl: 7
• boy: 5

Explanation:

Let g and b represent the numbers of candy canes the girl and boy have, respectively.

g -1 = b +1 . . . . . . girl gives to boy, they're equal

g +1 = 2(b -1) . . . . boy gives to girl; she has double

Adding 1 to the first equation gives an expression for g that can be substituted into the second equation.

g = b +2

(b +2) +1 = 2b -2

5 = b . . . . . . . . . . add 2-b, simplify

g = 5+2 = 7 . . . . . find g

The girl has 7 candy canes; the boy has 5.