Question

Lakshmi is trying to throw basketballs through hoops at a fair. If a ball goes through a hoop, she receives £50, but if it does not, she has to pay £20 for the shot. After 15 shots, Lakshmi finds she has made a profit of £1.20. How many times did Lakshmi successfully throw a ball through a hoop?

Answer 1

Lakshmi successfully threw the ball through the hoop 4 times after solving the system of equations based on the total number of shots and the monetary gains and losses.

Step-by-step explanation:

To determine how many times Lakshmi successfully threw a ball through a hoop, we can define two variables: let x be the number of successful shots, and y be the number of unsuccessful shots. Since Lakshmi took a total of 15 shots, we have the equation x + y = 15. Next, considering the money exchanged: for every successful shot Lakshmi earns £50, and for every unsuccessful shot, she loses £20. Her total profit was £1.20, leading to the second equation 50x - 20y = 1.20.

To solve this system of equations, we start by expressing y in terms of x from the first equation: y = 15 - x. Replacing y in the second equation gives us 50x - 20(15 - x) = 1.20. Simplifying and solving for x, we find that Lakshmi made x successful shots.

Let's solve the equation:

• 50x - 300 + 20x = 1.20
• 70x = 301.20
• x = 301.20 / 70
• x ≈ 4.31

Since Lakshmi can't make a fraction of a shot, we round down to get 4 successful shots. Therefore, Lakshmi successfully threw the ball through the hoop 4 times.