Question

Miriam and Ishak are having a competition throwing coins into a cup. Ishak made 48% of the coins into the cup. Miriam has already thrown 30 coins and only 12 made it into the cup. How many consecutive throws must make it into the cup in order for Miriam to beat Ishak?

Answer 1

Miriam must make at least 5 more consecutive successful throws to have a better success rate than Ishak's 48%.

Step-by-step explanation:

To figure out how many consecutive throws Miriam must make into the cup to beat Ishak's 48% success rate, we need to determine how many successful throws will give her a higher percentage than 48%. Ishak's rate suggests that if he threw 100 coins, he would make 48 into the cup. Miriam has already made 12 out of 30, which is 40%. To surpass Ishak, Miriam's percentage must become greater than 48%.

To calculate this, let's assume Miriam makes x consecutive successful throws after her initial 30 throws. After these additional successful throws, she will have 12 + x successful throws out of 30 + x total throws. We set up the inequality:

(12 + x) / (30 + x) > 0.48

Multiplying both sides by (30 + x) to clear the fraction, we get:

12 + x > 14.4 + 0.48x

Now, we solve for x:

x - 0.48x > 14.4 - 12

0.52x > 2.4

x > 2.4 / 0.52

x > 4.615

Since Miriam can't make a fraction of a throw, she will need to make at least 5 more consecutive successful throws to achieve a success rate greater than 48% and beat Ishak.