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Workings

Hint
What do the fractions add up to?

Answer
There are 980 coins in the collection.

Reasoning
Using fractions:

   ¹/₂ + ¹/₄ + ¹/₅ = ¹⁹/₂₀

The remaining ¹/₂₀ is 49 coins.

Therefore, the ²⁰/₂₀ must equal 20 lots of 49 = 980.

Alternative Reasoning
Using percentages:

   50% + 25% + 20% = 95%

The remaining 5% is 49 coins.

If 5% is 49 coins, 10% is 98 coins, 100% is 980 coins.

Double-Checking
¹/₂ of 980 is 490
¹/₄ of 980 is 245
¹/₅ of 980 is 196
and the remaining 49 coins.

And 490 + 245 + 196 + 49 = 980.

Workings

Hint
What do the 3 numbers add to, and multiply to, so far?

Answer
$0.50.

Reasoning
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.

The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.

You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.

The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P

    8.50 + P = 18.00 x P

        8.50 = 18.00 x P − P

        8.50 = 17.00 x P

8.50 ÷ 17.00 = P

           P = 0.50.

Workings

Hint
Which letters are missing?

Answer
The letter was written on a typewriter that has a problem with the top row of letters printing correctly. The letter should have read:

Dear Kevin,

I would like to complain about the top row of my typewriter.

These letters do not appear to be working correctly.

As you can see, they are missing from this document.

I would be very grateful if you could correct this problem immediately.

Kind regards.

Sam South.

Workings

Answer
6423 = 109,191 ÷ 17.

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 have been replaced by 7, 1, 8, 2, 4, 3, 5, 0, 6, 9 respectively.