Jetta has to get 58 using just threes and sevens. How many sevens go into 58? There are 8 and 2 over. Since 3 won’t go into two, she has to use fewer than 8 sevens.
Now seven sevens are 49 which leaves 9 over. But 9 = 3x3,
so 58 = 7x7 + 3x3. She can make 58.
We now work systematically to find all possible ways of making 58 using threes and sevens.
| Number of sevens | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
| Number of threes | 3 | 10 | 17 | ||||||
| x | 58 | x | x | 58 | x | x | 58 | x |
From the table we can see that there are 3 ways to make 58. These all involve the number of sevens decreasing by 3 while the number of threes increases by 7. Is this a coincidence?
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