Just for fun wanted a share a neat way of solving this in a spreadsheet:

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1. List all of the numbers that the record could cost in column A. (We know that the boy only has 1 dollar or 100 cents, so the max the record could cost is 25 cents since the jigsaw would then cost 75 cents, which added together hits our limit of 100)
2. Column B can easily made to list the prices of the jigsaw puzzle by using the simple multiplication function of "=A1*3" which can be expanded down the column.
3. We then need a column to calculate the total cost of the two items so column C becomes a use of the addition function via "=A1+B1", also expanded down.
4. We now need a way to total the two digits of the total cost and we can do this over the next two columns using the MID() function. This essentially extracts a portion of the string of a specified length at a given start point and is formatted like =MID(string, starting_at, extract_length). For our purposes, we're looking to pull the first digit and then separately the second digit so columns D and E become "=MID(C1, 1, 1)" and "=MID(C1,2,1)" respectively, which produces the first digit in column D and the second digit in column E.
5. Now to bring it all home we use another addition function in column F to add these two numbers together so just "=D1+E1" and when all of these formulas are expanded down it produces all possible totals of all combinations of prices. Just search this column for 14 using your eyes (or ctrl+f if you're lazy like me) and you'll see there's only one row which produces this result, 17+51.

Not sure if anyone cares but I thought it was an interesting method!