An athletic club had $$ \$ 14,200 $$ to spend on equipment. It purchased 5 bikes and 3 kayaks. The kayaks were $$ \$ 200 $$ more than twice the price of the bikes. There is $$ \$ 400 $$ left over. How much money did each kayak cost?

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Para resolver este problema, sigamos los pasos detalladamente:

**Datos del problema:**
- Presupuesto total: \$14,200
- Compra de equipo: 5 bicicletas y 3 kayaks
- Costo de los kayaks: \$200 más que el doble del precio de las bicicletas
- Dinero restante: \$400

**Objetivo:**
Determinar el costo de cada kayak.

**Pasos para la solución:**

1. **Definir las variables:**
   - Sea $$ B $$ el costo de una bicicleta.
   - Entonces, el costo de un kayak será $$ 2B + 200 $$ dólares.

2. **Calcular el gasto total en bicicletas y kayaks:**
   - Costo total de las bicicletas: $$ 5B $$
   - Costo total de los kayaks: $$ 3(2B + 200) = 6B + 600 $$

3. **Determinar el gasto total:**
   - Presupuesto inicial menos el dinero restante: $$ 14,200 - 400 = 13,800 $$ dólares
   - Por lo tanto, la ecuación será:
     $$
     5B + 6B + 600 = 13,800
     $$
     $$
     11B + 600 = 13,800
     $$

4. **Resolver la ecuación para $$ B $$:**
   $$
   11B = 13,800 - 600
   $$
   $$
   11B = 13,200
   $$
   $$
   B = \frac{13,200}{11}
   $$
   $$
   B = 1,200
   $$

- **Costo de una bicicleta ($$ B $$):** \$1,200

5. **Calcular el costo de cada kayak:**
   $$
   \text{Costo del kayak} = 2B + 200 = 2(1,200) + 200 = 2,400 + 200 = 2,600
   $$

- **Costo de cada kayak:** \$2,600

**Conclusión:**
Cada kayak costó **\$2,600**.
Cada kayak costó \$2,600.

An athletic club had to spend on equipment. It purchased 5 bikes
and 3 kayaks. The kayaks were more than twice the price of the bikes.
There is left over. How much money did each kayak cost?

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An athletic club had to spend on equipment. It purchased 5 bikes and 3 kayaks. The kayaks were more than twice the price of the bikes. There is left over. How much money did each kayak cost?