A class has 20 boys and 21 girls. The class as a whole has a GPA (grade point average) of 2.96, and the boys have a GPA of 2.40. What is the GPA of the girls? (Round your answer to two decimal places.)

Question

29-10-2022
Mathematics

contestada

A class has 20 boys and 21 girls. The class as a whole has a GPA (grade point average) of 2.96, and the boys have a GPA of 2.40. What is the GPA of the girls? (Round your answer to two decimal places.)

Respuesta :

Otras preguntas

Golden West Beverages Inc. is behind schedule in the implementation of a new accounting information system and management wants to get the project back on track

Define the following core-terms: Encryption

Antibiotic Resistance Student Handout 1. Describe how the process of natural selection has given rise to antibiotic-resistant bacteria. 2. What are some other e

How do you get an STI? Pick all that apply. a genital to genital contact b rectal fluid C breast milk d e 6 mouth to mouth contact urine sweat vaginal fluid sal

Symptoms of Fetal Alcohol Syndrome (FAS) do NOT include which of the following? thin upper lip shorter limbs for males short flat nose small eye openings

Average Daily Sunlight Hours Available For Solar Electric (Solar PV) Panels No Data Available MEXICO H Public Domain CUBA Hours 55 Hours 5 Hours 4.5 Hours 42 Ho

Of software architecture shows how the software is decomposed for development.O The logical viewO The process viewO The development viewO The physical view

Mildred Quinene received contact radiation of the nose. What is the correct code?A) D9Y17ZZB) D911BYZC) D9015ZZD) D9013ZZ

Pedro's client requires life insurance for five years only. Which of the following types of life insurance should he normally recommend?(Search Chapter 7)a.univ

Paychecks are created ______________.A) by clickingon the navigation bar and selecting Payroll B) by clicking Payroll on the navigation bar and selecting Run Pa

MalichiU19086 MalichiU19086 · Answer 1 · 2022-10-29T14:59:01+02:00

There are 20+21= 41 people on the class. Let B be the grade points of the boys and G be the grade points of the girls. Since the class has a whole GPA of 2.96, we can write

[tex]\frac{B+G}{41}=2.96[/tex]

On the other hand, the GPA of the boys is

[tex]\begin{gathered} \frac{B}{20}=2.40 \\ \text{then, the grade points of the boys is} \\ B=20\times2.40 \\ B=48 \end{gathered}[/tex]

By substituting this result into the first equation, we have

[tex]\frac{48+G}{41}=2.96[/tex]

After multiplying both sides by 41 and subtracting 48 in both sides, we get

[tex]\begin{gathered} 48+G=41\times2.96 \\ G=41\times2.96-48 \\ \text{then} \\ G=73.36 \end{gathered}[/tex]

Since the GPA of the girls is

[tex]\frac{G}{21}[/tex]

we get

[tex]\frac{73.36}{21}=3.49333[/tex]

Hence, by rounding down to the nearest hundredth, the answer is 3.49