Respuesta :
Answer:
greater than or equal [tex]46[/tex] to and less than [tex]96[/tex]
Step-by-step explanation:
GIVEN: On the first four exam your grades are [tex]76,78,73[/tex] and [tex]77[/tex]. You are hoping to earn a C in the course. This will occur if the average of your fifth exam grades is greater than or equal to [tex]70[/tex] and less than [tex]80[/tex].
TO FIND: range of grades on the fifth exam will result in earning a C.
SOLUTION:
Total number of marks scored till first four exams [tex]=76+78+73+77[/tex]
[tex]=304[/tex]
let average marks scored after fifth exam be [tex]S[/tex].
let marks scored in fifth exam be [tex]x[/tex]
[tex]S=\frac{76+78+73+77+x}{5}[/tex]
[tex]S=\frac{304+x}{5}[/tex]
Now, to earn a C the average must be greater than or equal to [tex]70[/tex] and less than [tex]80[/tex]
[tex]70\leq S< 80[/tex]
[tex]70\leq \frac{304+x}{5} <80[/tex]
when
[tex]\frac{304+x}{5}\geq 70[/tex]
[tex]304+x\geq 350[/tex]
[tex]x\geq 46[/tex]
when
[tex]\frac{304+x}{5}<80[/tex]
[tex]304+x<400[/tex]
[tex]x<96[/tex]
Hence grades in fifth exam must be greater than or equal [tex]46[/tex] to and less than [tex]96[/tex]
