Question

shureka washburn has scores of 79, 72, 80, and 53 on her algebra tests.
a. use an inequality to find the scores she must make on the final exam to pass the course with an average of 74 or higher.
b. explain the meaning of the answer to part (a).
a. the solution set is {x|x≥77}.(type an inequality.)
b. select the correct choice below and fill in the answer box to complete your choice.
○a. a final - exam grade of less than □ will result in an average of 74 or higher.
○b. a final - exam grade of □ or more will result in an average of 74 or higher.
○c. a final - exam grade of more than □ will result in an average of 74 or higher.
○d. a final - exam grade of □ or less will result in an average of 74 or higher.

Explanation:

Step1: Comprender la media

La media de las notas se calcula sumando todas las notas y dividiendo entre el número de notas. Aquí, tenemos 4 notas previas y la nota del examen final $x$, y queremos una media de 74 o más.

Step2: Escribir la desigualdad

La media es $\frac{79 + 72+80 + 53+x}{5}\geq74$. Simplificando el numerador de la izquierda, tenemos $\frac{284 + x}{5}\geq74$.

Step3: Resolver la desigualdad

Multiplicamos ambos lados por 5: $284 + x\geq370$. Luego restamos 284 de ambos lados: $x\geq370 - 284$, lo que da $x\geq77$. Esto significa que una nota de 77 o más en el examen final dará una media de 74 o más para el curso.

Answer:

a. La solución correcta ya está dada: $\{x|x\geq77\}$
b. B. A final exam grade of 77 or more will result in an average of 74 or higher.