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.
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Puzzle 110
In Farmer Stone's hay loft, there were several animals, in particular birds, mice, and cockroaches.
One day, feeling bored, I decided to count the animals. I found there were exactly 150 feet and 50 heads in total, and there were twice as many cockroaches as mice.
Kelly beat Sam in both games, and Reed beat Jamie in both games. The winner in game 1 came second in game 2. Reed won game 2, and Jamie beat Sam in game 1. No player got the same placing twice.
Can you determine who finished where in each game?