Solve It like the way form two students solve it

Mathematics

ScanSolve AI Answer

Answers

2 parts
a(i)

50\text{50}

a(ii)

130\text{130}

Step-by-step solution

5 steps

Okay, let's solve this problem step-by-step, focusing on direct calculations.

We are given:

  • Total students in class = 255
  • Students who studied English only = 125
  • Students who studied Mathematics only = 80
  • Every student studied at least one subject.

Part a(i)· 3 steps

How many students studied both subjects?

  1. Find the total number of students who studied only one subject.

    Students (English only)+Students (Mathematics only)=125+80=205\text{Students (English only)} + \text{Students (Mathematics only)} = 125 + 80 = 205

  2. Since every student studied at least one subject, the total number of students is the sum of those who studied only one subject and those who studied both subjects.

    Total students=Students (only one subject)+Students (both subjects)\text{Total students} = \text{Students (only one subject)} + \text{Students (both subjects)} 255=205+Students (both subjects)255 = 205 + \text{Students (both subjects)}

  3. Calculate the number of students who studied both subjects.

    Students (both subjects)=255−205=50\text{Students (both subjects)} = 255 - 205 = 50

    The number of students who studied both subjects is 50\boxed{\text{50}}.

Part a(ii)

130\text{130}

How many students studied Mathematics?

  1. The total number of students who studied Mathematics includes those who studied Mathematics only and those who studied both subjects.

    Students (Mathematics)=Students (Mathematics only)+Students (both subjects)\text{Students (Mathematics)} = \text{Students (Mathematics only)} + \text{Students (both subjects)}

  2. Substitute the known values.

    Students (Mathematics)=80+50\text{Students (Mathematics)} = 80 + 50 Students (Mathematics)=130\text{Students (Mathematics)} = 130

    The number of students who studied Mathematics is 130\boxed{\text{130}}.

Part b

Draw a Venn diagram to represent the information.

Imagine two overlapping circles inside a rectangle.

  • The rectangle represents the total class of 255 students.

  • One circle represents English (E), and the other represents Mathematics (M).

  • In the part of the English circle that does not overlap with the Mathematics circle (English only), write 125.

  • In the part of the Mathematics circle that does not overlap with the English circle (Mathematics only), write 80.

  • In the overlapping region of the two circles (both subjects), write 50.

  • Since every student studied at least one subject, there are no students outside the circles but inside the rectangle.

To check: 125+80+50=255125 + 80 + 50 = 255, which is the total number of students.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QPlease give me the way the form two students solve ItQSolve it in short wayQSolve in the way that I can explain it to my lecturer
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.