Question

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Explanation:

Calculate Chloe's weekly cost

We use Multi-Step Word Problems to find the weekly cost.
Chloe attends camp for \(n\) weeks and registers for two workshops each week.
The base camp cost is \(85\) dollars per week.
The cost for two workshops is \(2 \times 5.50 = 11\) dollars per week.
The total weekly cost is:

$$ 85 + 11 = 96 \text{ dollars/week} $$

Solve for Chloe's weeks \(n\)

We use One-Step Equations to solve for \(n\).
The total charge is \(768\) dollars.

$$ 96n = 768 $$

$$ n = \frac{768}{96} = 8 $$

Calculate Lailan's total cost

We use Mixed Operations to find Lailan's total cost.
Lailan attends for \(6\) weeks and registers for three workshops each week.
The cost for three workshops is a flat rate of \(15\) dollars per week.
The total weekly cost is:

$$ 85 + 15 = 100 \text{ dollars/week} $$

For \(6\) weeks, the total charge is:

$$ 6 \times 100 = 600 \text{ dollars} $$

Set up equations for Ailee

Let \(B\) be the cost of band camp, \(S\) be the cost of soccer camp, and \(C\) be the cost of cheerleading camp.
The total cost for all three camps is equal to Lailan's total charge:

$$ B + S + C = 600 $$

We are given:

1. \(B = S + 100\)
2. \(C = \frac{1}{4}(B + S)\)

Solve for Ailee's band camp cost

Substitute \(B + S = 4C\) into the total cost equation:

$$ 4C + C = 600 \implies 5C = 600 \implies C = 120 $$

Thus, the sum of band and soccer camp costs is:

$$ B + S = 480 $$

Substitute \(S = B - 100\) into this sum:

$$ B + (B - 100) = 480 \implies 2B = 580 \implies B = 290 $$

Answer:

Question 1

The value of \(n\) is 8.

Question 2

Lailan's total charge is 600 dollars.

Question 3

The total cost of Ailee's band camp enrollment is 290 dollars.