Question

At the end of the semester, Jane Doe gets an 85% on her math test. She also gets 95% on her homework. Her teacher says that assessments are worth 90% of her grade, and homework is worth 10%. What is her grade in the class? Show your work.

Answer 1

Answer:

Marks of Jane Doe at the end of semester:

→ Assessment (Tests) = 85%

→ Homework = 95%

According to the teacher, the grades are alloted on the ratio as follows:

→ Assessment = 90% of Total Marks scored

→ Homework = 10% of Total Marks scored

Final Marks are just like converting marks of Assessment (which was totalled for 100 marks) to a total of 90 marks, and the homework (which was totalled for 100 marks) to a total of 10 marks.

Jane has scored 85 for 100 marks in her tests. Converting the score for a total of 90 we get:

⇒ 85 : 100 :: x : 90

⇒ 100 x = 90 × 85

⇒ 100 x = 7650

⇒ x = 7650 / 100

⇒ x = 76.5% in Assessment

For Homework, we get:

⇒ 95 : 100 :: x : 10

⇒ 100 x = 95 × 10

⇒ 100 x = 950

⇒ x = 950 / 100

⇒ x = 9.5% in Homework

Adding both the marks, we get:

⇒ Total = 76.5 + 9.5

⇒ Total = 86%

Hence the total grades or marks secured by Jane Doe collectively at the end of her semester is 86%.

Answer 2

Answer:

Given :-

• At the end of the semester, Jane Doe gets an 85% on her math test. She also gets 95% on her homework.
• Teacher says that assessments are worth 90% of her grade, and homework is worth 10%.

To Find :-

• What is her total grade in the class.

Solution :-

Given :

$\leadsto$ At the end of the semester, Jane Doe gets :

• Math test = 85%
• Homework = 95%

Again,

$\leadsto$ Teacher says that assessments are worth total grade :

• Math test = 90%
• Homework = 10%

$\longmapsto$ In case of Math test :

Let, the marks percentage he get in math test be x

According to the question,

↦ $\sf 85 : 100 : : x : 90$

↦ $\sf \dfrac{85}{100} =\: \dfrac{x}{90}$

By doing cross multiplication we get,

↦ $\sf 100 \times x =\: 85 \times 90$

↦ $\sf 100x =\: 7650$

↦ $\sf x =\: \dfrac{765\cancel{0}}{10\cancel{0}}$

↦ $\sf x =\: \dfrac{\cancel{765}}{\cancel{10}}$

↦ $\sf x =\: \dfrac{153}{2}$

➠ $\sf\bold{\pink{x =\: 76.5\%}}$

Hence, the mark percentage s he get in math test is 76.5%.

Again,

$\longmapsto$ In case of homework :

Let, the marks percentage he gets in homework be x

According to the question,

↦ $\sf 95 : 100 : : x : 10$

↦ $\sf \dfrac{95}{100} =\: \dfrac{x}{10}$

By doing cross multiplication we get,

↦ $\sf 100 \times x =\: 95 \times 10$

↦ $\sf 100x =\: 950$

↦ $\sf x =\: \dfrac{95\cancel{0}}{10\cancel{0}}$

↦ $\sf x =\: \dfrac{\cancel{95}}{\cancel{10}}$

↦ $\sf x =\: \dfrac{19}{2}$

➠ $\sf\bold{\pink{x =\: 9.5\%}}$

Hence, the mark percentage he gets in homework is 9.5%.

Now, we have to find the total grade he get in class :

$\implies \sf Total\: grade =\: Marks\: percentage\: in\: math\: test\: +\: Marks\: percentage\: in\: homework$

$\implies \sf Total\: grade =\: 76.5 + 9.5$

$\implies \sf Total\: grade =\: \dfrac{765}{10} + \dfrac{95}{10}$

$\implies \sf Total\: grade =\: \dfrac{765 + 95}{10}$

$\implies \sf Total\: grade =\: \dfrac{86\cancel{0}}{1\cancel{0}}$

$\implies \sf\bold{\red{Total\: grade\: =\: 86\%}}$

$\therefore$ The total grade Jane Doe gets in the class is 86%.