H.O.T. Problems Higher Dider Thinking 15. Persevere with Problems The experimental probability of a penny landing on tails is \( \frac{9}{16} \). If the penny landed on heads 21 times, how many times was the coin tossed?

Given that the experimental probability of a penny landing on tails is \( \frac{9}{16} \), we can set up the following equation to find the total number of times the coin was tossed: \[ \frac{9}{16} = \frac{\text{Number of times landed on tails}}{\text{Total number of times tossed}} \] Let's denote the total number of times the coin was tossed as \( x \). We are given that the penny landed on heads 21 times, so the number of times it landed on tails is \( x - 21 \). Substitute the values into the equation: \[ \frac{9}{16} = \frac{x - 21}{x} \] Now, we can solve for \( x \) to find the total number of times the coin was tossed. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{9}{16}=\frac{x-21}{x}\) - step1: Find the domain: \(\frac{9}{16}=\frac{x-21}{x},x\neq 0\) - step2: Swap the sides: \(\frac{x-21}{x}=\frac{9}{16}\) - step3: Cross multiply: \(\left(x-21\right)\times 16=x\times 9\) - step4: Simplify the equation: \(16\left(x-21\right)=9x\) - step5: Expand the expression: \(16x-336=9x\) - step6: Move the variable to the left side: \(16x-336-9x=0\) - step7: Subtract the terms: \(7x-336=0\) - step8: Move the constant to the right side: \(7x=0+336\) - step9: Remove 0: \(7x=336\) - step10: Divide both sides: \(\frac{7x}{7}=\frac{336}{7}\) - step11: Divide the numbers: \(x=48\) - step12: Check if the solution is in the defined range: \(x=48,x\neq 0\) - step13: Find the intersection: \(x=48\) The total number of times the coin was tossed is 48.