Question

Today, Richard ate 7 fewer than twice the number of candies his brother Carlos ate *yesterday. If Carlos ate 5 more candies to- day than he did yesterday, how many can- dies did Carlos eat today if Richard ate 13 candies today?

Answer 1

Answer: Carlos ate 15 candies today.

Explanation:

Step 1: Let's denote the number of candies Carlos ate yesterday as
`\( c \)`.

Step 2: According to the problem, Richard ate 7 fewer than twice the number of candies Carlos ate yesterday. This can be represented as:

`\[ \text{Richard's candies} = 2c - 7 \]`

Step 3: We're given that Richard ate 13 candies today. So, we can set up the equation:

`\[ 2c - 7 = 13 \]`

Step 4: The problem also states that Carlos ate 5 more candies today than he did yesterday. This can be represented as:

`\[ \text{Carlos's candies today} = c + 5 \]`

Using the information provided, we can solve for
`\( c \)` (the number of candies Carlos ate yesterday) and then determine how many candies Carlos ate today.

From the equation
`\(2c - 7 = 13\)`, we find that
`\(c = 10\)`. This means Carlos ate 10 candies yesterday.

Now, given that Carlos ate 5 more candies today than he did yesterday, we can determine the number of candies Carlos ate today:

`\[ \text{Carlos's candies today} = c + 5 \]`

`\[ \text{Carlos's candies today} = 10 + 5 = 15 \]`