Acceso
Prima
Hogar Banco de preguntas Matemáticas Álgebra
Pregunta
upstudy study bank question image url

49. Write an equation to represent each of the situations described below. a. On Friday, 150 people went to see "Ode to Algebra" performed in the school auditorium. Both \( c \) children and \( a \) adults attended the performance b. The cost of a new CD is \( \$ 14.95 \), and the cost of a video game is \( \$ 39.99 \). Wade spent \( \$ 84.84 \) on \( c \) CDs and \( v \) video games.

Ask by Thornton Willis. in the United States
Jan 27,2025

Solución de tutoría real

Respuesta verificada por el tutor

Responder

a. \( c + a = 150 \) b. \( 14.95c + 39.99v = 84.84 \)

Solución

Sure, let's break down each situation and formulate the corresponding equations. ### a. Attendance at "Ode to Algebra" **Situation:** - Total attendees: 150 - Let \( c \) represent the number of children. - Let \( a \) represent the number of adults. **Equation:** The total number of people is the sum of children and adults attending the performance. \[ c + a = 150 \] ### b. Cost of CDs and Video Games **Situation:** - Cost of one CD: \$14.95 - Cost of one video game: \$39.99 - Total amount Wade spent: \$84.84 - Let \( c \) represent the number of CDs bought. - Let \( v \) represent the number of video games bought. **Equation:** The total cost is the sum of the cost of CDs and the cost of video games. \[ 14.95c + 39.99v = 84.84 \] --- **Summary of Equations:** a. \( c + a = 150 \) b. \( 14.95c + 39.99v = 84.84 \)

Revisado y aprobado por el equipo de tutoría de UpStudy

error msg
Explicar
Simplifique esta solución

Extra Insights

For the first situation, the equation representing the total number of attendees can be written as \( c + a = 150 \). This means that the combined count of children and adults equals the total attendance at the performance. In the second situation, the equation for the total amount spent by Wade can be expressed as \( 14.95c + 39.99v = 84.84 \). This equation accounts for the cost of \( c \) CDs and \( v \) video games, summing up to the total expenditure.

preguntas relacionadas

Expand and simplify: (1) \( \quad(2 x+y)^{2}-(3 x-2 y) \)
Álgebra South Africa Jan 30, 2025
29 Förenkla uttrycket \( \frac{(a+1)^{7}-(a+1)^{5}}{a(a+2)} \) så långt som möjligt.
Álgebra Sweden Jan 30, 2025
\( \begin{array}{ll}\text { 1) } a^{1}-a^{2} b & \text { 1) } 5 x^{3} y^{3}-20 x y^{2} \\ \text { m) } 3 x^{2}-6 x^{3}+9 x^{4} & \text { n) } 4 p q^{2}-8 p q-12 p^{2} q \\ \text { a) } 5 a^{2}-10 a b+5 b^{2} & \text { p) } 3 a^{2}-6 a+9 \\ \text { q) }-6 a b^{1}+4 c b^{2}-2 d b & \text { r) } 7 x^{2} y^{2}-35 x y^{2} z-28 y \\ \text { s) } 16 a^{4} b^{8}-8 a^{3} b^{7}+36 a^{2} b^{3} & \text { t) } 4 \pi R^{2}-8 \pi R \\ \text { u) } \frac{1}{4} a^{2} b^{3}-\frac{1}{16} a^{3} b^{2} & \text { v) } 9 x^{3} y z^{2}+3 x y z-18 x\end{array} \)
Álgebra South Africa Jan 30, 2025
Simplify the following without using a calculator: (a) \( \sqrt{7} \sqrt{3} \) (b) \( \quad \sqrt{7} \sqrt{7}+(\sqrt{11})^{2} \) (c) \( \quad(2 \sqrt{3})^{2} \) (d) \( 3 \sqrt{6}-\sqrt{6}+7 \sqrt{6} \) (e) \( \sqrt[4]{3}+7 \sqrt[4]{3}-5 \sqrt[4]{3} \) (f) \( \sqrt{3}+\sqrt{27} \) (g) \( 2 \sqrt{18}-\sqrt{32} \) (h) \( \frac{\sqrt{32}}{\sqrt{2}} \) (i) \( \frac{\sqrt[3]{51}}{\sqrt[3]{3}} \) (j) \( \frac{\sqrt{32}}{2} \) (k) \( \frac{\sqrt{54}}{9} \) (1) \( \frac{\sqrt{8}+\sqrt{2}}{\sqrt{2}} \) (m) \( \frac{\sqrt{50}-\sqrt{2}}{\sqrt{8}} \) (n) \( \frac{\sqrt[3]{16}-\sqrt[3]{54}}{\sqrt[3]{2}} \) (o) \( \frac{\sqrt{48}-\sqrt{32}}{\sqrt{12}-\sqrt{8}} \) (p) \( \quad(5-\sqrt{3})(5+\sqrt{3}) \) (q) \( (5-\sqrt{3})^{2} \) (r) \( \quad(5 \sqrt{2}-\sqrt{3})^{2} \) (s) \( \quad 2 \sqrt{5}(\sqrt{5}-3 \sqrt{20}) \) (t) \( \quad(\sqrt{5}+2 \sqrt{3})^{2}-(\sqrt{5}-2 \sqrt{3})^{2} \) (u) \( 2 \sqrt{8 m}(\sqrt{2 m}-3 \sqrt{18 m})\left(\right. \) v) \( \frac{10 \sqrt{2 x^{20}}+7 \sqrt{8 x^{20}}}{\sqrt{18 x^{20}}} \)
Álgebra South Africa Jan 30, 2025
The sum of two numbers is 25 and their difference is -5 . What are the two numbers? Let \( x= \) one number and \( y= \) the other number. The corresponding modeling system is \( \left\{\begin{array}{l}x+y=25 \\ x-y=-5\end{array}\right. \). Solve the system graphically.
Álgebra United States Jan 30, 2025

Latest Algebra Questions

29 Förenkla uttrycket \( \frac{(a+1)^{7}-(a+1)^{5}}{a(a+2)} \) så långt som möjligt.
Álgebra Sweden Jan 30, 2025
The sum of two numbers is 25 and their difference is -5 . What are the two numbers? Let \( x= \) one number and \( y= \) the other number. The corresponding modeling system is \( \left\{\begin{array}{l}x+y=25 \\ x-y=-5\end{array}\right. \). Solve the system graphically.
Álgebra United States Jan 30, 2025
\( \begin{array}{ll}\text { 1) } a^{1}-a^{2} b & \text { 1) } 5 x^{3} y^{3}-20 x y^{2} \\ \text { m) } 3 x^{2}-6 x^{3}+9 x^{4} & \text { n) } 4 p q^{2}-8 p q-12 p^{2} q \\ \text { a) } 5 a^{2}-10 a b+5 b^{2} & \text { p) } 3 a^{2}-6 a+9 \\ \text { q) }-6 a b^{1}+4 c b^{2}-2 d b & \text { r) } 7 x^{2} y^{2}-35 x y^{2} z-28 y \\ \text { s) } 16 a^{4} b^{8}-8 a^{3} b^{7}+36 a^{2} b^{3} & \text { t) } 4 \pi R^{2}-8 \pi R \\ \text { u) } \frac{1}{4} a^{2} b^{3}-\frac{1}{16} a^{3} b^{2} & \text { v) } 9 x^{3} y z^{2}+3 x y z-18 x\end{array} \)
Álgebra South Africa Jan 30, 2025
\( i \quad ( y + 5 ) ^ { 2 } \)
Álgebra South Africa Jan 30, 2025
\( 4.3 ^ { x } + 3 ^ { x } = 15 \)
Álgebra South Africa Jan 30, 2025
Anterior Próximo
¡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