6p+11q+4
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There are 31 ways:1p × 211p × 19 + 2p × 11p × 17 + 2p × 21p × 16 + 5p × 11p × 15 + 2p × 31p × 14 + 2p × 1 + 5p × 11p × 13 + 2p × 41p × 12 + 2p × 2 + 5p × 11p × 11 + 2p × 51p × 11 + 5p × 21p × 10 + 2p × 3 + 5p × 11p × 9 + 2p × 61p × 9 + 2p × 1 + 5p × 21p × 8 + 2p × 4 + 5p1p × 7 + 2p × 71p × 7 + 2p × 2 + 5p × 21p × 6 + 2p × 5 + 5p1p × 6 + 5p × 31p × 5 + 2p × 81p × 5 + 2p × 3 + 5p × 21p × 4 + 2p × 6 + 5p × 11p × 4 + 2p × 1 + 5p × 31p × 3 + 2p × 91p × 3 + 2p × 4 + 5p × 21p × 2 + 2p × 7 + 5p × 11p × 2 + 2p × 2 + 5p × 31p × 1 + 2p × 101p × 1 + 2p × 5 + 5p × 21p × 1 + 5p × 42p × 8 + 5p × 12p × 3 + 5p × 3
Reduce the second part by taking 8 out. (11p + 8)/6 = p - 2 Multiply both sides by 6. 11p + 8 = 6p - 12 Subtract 6p from both sides. 5p + 8 = -12 Subtract 8 from both sides. 5p = -20 Divide both sides by 5. p = -4 Check it by substituting -4 for p in the original equation. (-44 + 8)/6 = (-32 - 16)/8 -36/6 = -48/8 -6 = -6 It checks.
5p + 4y
7p + 2 = 5p + 8 7p - 5p = 8 - 2 2p = 6 p = 3
Well, isn't that a happy little riddle! If one of the coins is not a 10p coin, then it must be a 1p coin. So, you have a 10p coin and a 1p coin in your hand, making a total of 11p. Just like painting, sometimes it's the small details that make the big picture come together beautifully.