### Five Coins

Ben has five coins in his pocket. How much money might he have?

### Christmas Shopping

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

# Weekly Problem 48 - 2009

##### Stage: 2 and 3 Short Challenge Level:

Suppose Dan gives Ann $x$ £$2$ coins and Ann gives Dan $y$ £$5$ coins. Then Dan has £$(18-2x+5y)$ and Ann has £$(40-5y+2x)$.

We need $18-2x+5y=40-5y+2x\Rightarrow 10y-4x=22\Rightarrow 5y-2x=11$. The solution to this equation which minimises $x+y$ is $x=2$, $y=3$, so the smallest number of coins that must change hands is $5$.

This problem is taken from the UKMT Mathematical Challenges.

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