Kalai threw a ball at a hoop 30 times. One point was scored when the ball passed
through the hoop and one point was deducted when the bali did not.
For Kalai’s first 25 throws, the ball passed through the hoop 20 times.
(a) What was Kalai’s score from the first 25 throws?
(b) At the end of 30 throws, Kalai scored 18 points. How many times did the ball pass
through the hoop for her last 5 throws?

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UpStudy AI · Accepted Answer

Let's break down the problem step by step.

### Known Conditions:
1. Kalai threw the ball 30 times in total.
2. One point is scored for each successful throw (ball through the hoop) and one point is deducted for each unsuccessful throw (ball not through the hoop).
3. For the first 25 throws:
   - The ball passed through the hoop 20 times.
   - Therefore, it did not pass through the hoop $$25 - 20 = 5$$ times.
4. At the end of 30 throws, Kalai scored 18 points.

### Part (a): Score from the First 25 Throws
To calculate Kalai's score from the first 25 throws, we can use the formula:

$$
\text{Score} = (\text{Points Scored}) - (\text{Points Deducted})
$$

Where:
- Points Scored = Number of successful throws = 20
- Points Deducted = Number of unsuccessful throws = 5

Now, substituting the values:

$$
\text{Score} = 20 - 5 = 15
$$

So, Kalai's score from the first 25 throws is **15 points**.

### Part (b): Successful Throws in the Last 5 Throws
We know that at the end of 30 throws, Kalai scored 18 points. We can find out how many successful throws she made in the last 5 throws by first determining her score from those throws.

Let $$x$$ be the number of successful throws in the last 5 throws. Then, the number of unsuccessful throws would be $$5 - x$$.

The total score from the last 5 throws can be expressed as:

$$
\text{Score from last 5 throws} = x - (5 - x) = 2x - 5
$$

Now, we can set up the equation for the total score:

$$
\text{Total Score} = \text{Score from first 25 throws} + \text{Score from last 5 throws}
$$

Substituting the known values:

$$
18 = 15 + (2x - 5)
$$

Now, let's solve for $$x$$:

$$
18 = 15 + 2x - 5
$$
$$
18 = 10 + 2x
$$
$$
18 - 10 = 2x
$$
$$
8 = 2x
$$
$$
x = 4
$$

Thus, Kalai passed through the hoop **4 times** in her last 5 throws.

### Summary of Answers:
(a) Kalai's score from the first 25 throws is **15 points**.  
(b) Kalai passed through the hoop **4 times** in her last 5 throws.
(a) Kalai scored **15 points** from the first 25 throws. (b) Kalai passed through the hoop **4 times** in her last 5 throws.

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