Pregunta
upstudy study bank question image url

1.2 Homework Question 7, 1.2.63 , How many ounces of a \( 15 \% \) alcohol solution must be mixed with 13 ounces of a \( 20 \% \) alcohol solution to make a \( 16 \% \) alcohol solution? 0 of \( 1 \leftarrow \) Po.

Ask by Pollard Gonzalez. in the United States
Jan 24,2025

Solución de tutoría real

Respuesta verificada por el tutor

Responder

You need to mix 52 ounces of the 15% alcohol solution with 13 ounces of the 20% alcohol solution to get a 16% alcohol solution.

Solución

To determine how many ounces of a **15%** alcohol solution need to be mixed with **13 ounces** of a **20%** alcohol solution to obtain a **16%** alcohol solution, let's set up the equation based on the concentration of alcohol in each solution. **Let \( x \) be the number of ounces of the 15% solution needed.** 1. **Calculate the amount of pure alcohol in each solution:** - **15% solution:** \( 0.15x \) ounces of alcohol - **20% solution:** \( 0.20 \times 13 = 2.6 \) ounces of alcohol 2. **Total volume and desired concentration:** - **Total volume:** \( x + 13 \) ounces - **Desired alcohol concentration:** 16%, so total pure alcohol needed is \( 0.16(x + 13) \) ounces 3. **Set up the equation:** \[ 0.15x + 2.6 = 0.16(x + 13) \] 4. **Solve for \( x \):** \[ 0.15x + 2.6 = 0.16x + 2.08 \] \[ 2.6 - 2.08 = 0.16x - 0.15x \] \[ 0.52 = 0.01x \] \[ x = \frac{0.52}{0.01} = 52 \] **Conclusion:** You need to mix **52 ounces** of the **15%** alcohol solution with **13 ounces** of the **20%** alcohol solution to obtain a **16%** alcohol solution. **Answer:** 52 ounces of the 15 % alcohol solution are needed.

Revisado y aprobado por el equipo de tutoría de UpStudy

error msg
Explicar
Simplifique esta solución

The Deep Dive

To solve this problem, we can use the formula for mixing solutions. Let's denote the amount of the \( 15\% \) solution as \( x \) ounces. The \( 15\% \) solution contains \( 0.15x \) ounces of alcohol, and the \( 20\% \) solution contains \( 0.20(13) = 2.6 \) ounces of alcohol. We want the final mixed solution to be \( 16\% \). The total volume of the solution will be \( x + 13 \) ounces, and the total amount of alcohol in the mixture will be \( 0.15x + 2.6 \) ounces. So, we set up the equation: \[ \frac{0.15x + 2.6}{x + 13} = 0.16 \] Cross-multiplying gives us: \[ 0.15x + 2.6 = 0.16(x + 13) \] Expanding and solving for \( x \): \[ 0.15x + 2.6 = 0.16x + 2.08 \] Rearranging terms leads to: \[ 2.6 - 2.08 = 0.16x - 0.15x \] \[ 0.52 = 0.01x \] Thus, \( x = \frac{0.52}{0.01} = 52 \) ounces. So, you need to mix **52 ounces** of the \( 15\% \) alcohol solution with 13 ounces of the \( 20\% \) alcohol solution to achieve a \( 16\% \) alcohol solution!

¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde Hazte Premium
Estudiar puede ser una verdadera lucha
¿Por qué no estudiarlo en UpStudy?
Seleccione su plan a continuación
Prima

Puedes disfrutar

Empieza ahora
  • Explicaciones paso a paso
  • Tutores expertos en vivo 24/7
  • Número ilimitado de preguntas
  • Sin interrupciones
  • Acceso completo a Respuesta y Solución
  • Acceso completo al chat de PDF, al chat de UpStudy y al chat de navegación
Básico

Totalmente gratis pero limitado

  • Solución limitada
Bienvenido a ¡Estudia ahora!
Inicie sesión para continuar con el recorrido de Thoth AI Chat
Continuar con correo electrónico
O continuar con
Al hacer clic en "Iniciar sesión", acepta nuestros términos y condiciones. Términos de Uso & Política de privacidad