The Smart Scholars Method

3a + 5p = M(23) means a = [M(23) – 5p]/3.

7a + 4p = 7[M(23) – 5p]/3 + 4 p = [M(23) – 23p]/3 = M(23).

This is not true of any other given combinations.

Sanity check

One case where 3a + 5p = M(23) is when a = 12 and p = 2, as 3*12 + 5*2 = 46 = M(23). Then 7a + 4p = 7*12 + 4*2 = 92 = M(23).

Or, when a = 7 and p = 5, 3a + 5p = M(23) is as 3*7 + 5*5 = 46 = M(23). Then 7a + 4p = 7*7 + 4*5 = 69 = M(23).

Again, when a = 2 and p = 8, 3a + 5p = M(23) is as 3*2 + 5*8 = 46 = M(23). Then 7a + 4p = 7*2 + 4*8 = 46 = M(23).

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