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?
(16)/(18+T)= 1/1.5
16*1.5=18+T
24=18+T
T=6
To solve this problem, we need to determine the number of tails up coins and the total number of coins. Let's break it down step by step:
Step 1: Start with the given information.
- We have 16 coins that are heads up.
- We have 18 coins that are tails up.
- We want to add some coins that are tails up to reach a ratio of 1 head up to 1.5 tails up.
Step 2: Set up the equation for the desired ratio.
- Let's assume the number of tails up coins we need to add is "x."
The ratio of heads up to tails up coins after adding x tails up coins is 1:1.5, which can be written as (16 / (18 + x)) = 1 / 1.5.
Step 3: Solve the equation.
- Cross-multiply to remove the fractions:
16 * 1.5 = (18 + x) * 1.
- Simplify the equation:
24 = 18 + x.
- Solve for x:
x = 24 - 18.
x = 6.
Step 4: Calculate the number of tails up coins and the total number of coins.
- The number of tails up coins is given as 18, and we added 6 more tails up coins, so the total number of tails up coins is 18 + 6 = 24.
- The total number of coins is the sum of heads up and tails up coins:
Total = 16 + 24 = 40.
So, there are 24 coins that are tails up, and the total number of coins is 40.