You have 16 coins that are heads up and 18 coins that are tails up. After you add some coins that are tails up, the ratio of heads up to tails up is 1 to 1.5. How many coins are tails up? How many coins in all?
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solve for T, add that to 18 to get the number of tails.
Let's begin solving the problem step by step:
Step 1: Let's assume the number of coins that are tails up after adding some is 'x'.
Step 2: Initially, we have 16 coins that are heads up and 18 coins that are tails up, making a total of 34 coins.
Step 3: After adding 'x' coins, the number of coins that are heads up and tails up will remain the same, as the ratio of heads up to tails up is 1 to 1.5, or simplifying, 2 to 3.
Step 4: We can set up the following equation based on the given information:
16 / (18 + x) = 2 / 3
Step 5: Cross-multiplying the equation gives us:
16 * 3 = 2 * (18 + x)
Step 6: Simplifying the equation:
48 = 36 + 2x
Step 7: Subtracting 36 from both sides:
12 = 2x
Step 8: Dividing both sides by 2:
x = 6
Therefore, there are 6 coins that are tails up after adding some.
Step 9: To find the total number of coins, we add the initial number of coins (34) to the additional tails up coins (6):
Total number of coins = 34 + 6 = 40
Therefore, there are a total of 40 coins.
In conclusion, there are 6 coins that are tails up and the total number of coins is 40.
To solve this problem, we need to find out how many coins in total, as well as the number of coins that are tails up.
Let's start by representing the number of coins that are tails up as 't' and the number of coins that are heads up as 'h'.
From the given information, we know that initially there are 16 coins that are heads up (h = 16) and 18 coins that are tails up (t = 18).
Now, let's add some coins that are tails up to the existing ones. The ratio of heads up to tails up after adding these new coins is 1 to 1.5, which means the total number of coins should be in the ratio of 1 to 2.5 (1 + 1.5).
Let's represent the total number of coins as 'n'.
We can set up the following equation based on the given information:
h + t (initial number of coins) = n (total number of coins)
16 + 18 = n
n = 34
Next, we need to find the number of coins that are tails up. We know that the ratio of heads up to tails up should be 1 to 1.5. This means:
h : t = 1 : 1.5
Dividing both sides of the equation by 'h', we get:
t = 1.5h
Since we know that h = 16, we can substitute this value into the equation to find the number of coins that are tails up:
t = 1.5 * 16 = 24
So, there are 24 coins that are tails up, and the total number of coins is 34.