Login
Premium
Home Question Bank Math Algebra
Question
upstudy study bank question image url

At the Heights School, the Maths club has 15 members and the Science club has 12. If a total of 13 students belong to only one of the two clubs, how many be- long to both clubs?

Ask by Estrada Brewer. in Australia
Dec 02,2024

Real Tutor Solution

Tutor-Verified Answer

Answer

The number of students who belong to both clubs is 7.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Reviewed and approved by the UpStudy tutoring team

The Deep Dive

To solve this problem, we can set some variables. Let \( x \) represent the number of students who belong to both clubs. Given that there are 15 members in the Maths club and 12 in the Science club, we can denote: - Students in only the Maths club = \( 15 - x \) - Students in only the Science club = \( 12 - x \) According to the problem, the total number of students who belong to only one of the two clubs is 13. Therefore, we can create the equation: \[ (15 - x) + (12 - x) = 13 \] Simplifying this, we get: \[ 27 - 2x = 13 \] Now, solving for \( x \): \[ 27 - 13 = 2x \\ 14 = 2x \\ x = 7 \] Thus, the number of students who belong to both clubs is 7.

Related Questions

Solve: \( \begin{array}{l}\frac{1}{b^{2}-3 b}+\frac{1}{b-3}=\frac{3}{b^{2}-3 b} \\ 0 \\ \frac{7}{2} \\ -\frac{5}{6} \\ 2\end{array} \)
Algebra United States Jan 22, 2025
EXERCISE 4 Fully simplify each of the following expres 1. \( (2 x+y)\left(3 x^{2}+2 x y+5 y^{2}\right) \) 3. \( (x-y)(3 x-2 x y+4) \) 5. \( (7 m-3 n)\left(5 m^{2}-2 m m-7 n^{2}\right) \) 7. \( (2 x-y)\left(4 x^{2}+2 x y-y^{2}\right) \) 9. \( (4 m-n)\left(2 m^{2}-3 m m-n^{2}\right) \) 11. \( (2 x-y)(2 x+y)(3 x-5 x y-y) \) 13. \( (9 m-n)\left(3 m^{2}-m m+2 n^{2}\right) \) 15. \( 5(a-b)\left(a^{2}+a b+b^{2}\right) \) 17. \( 2(3 p+q)\left(9 p^{2}-3 p q+q^{2}\right) \) 19. \( 3(2 x+1)\left(x^{2}-5 x-1\right) \) 1
Algebra South Africa Jan 22, 2025
3) Completa los coeficientes que hacen verdadera la igualdad. \( \begin{array}{l}\text { a) }(x+8)(x+3)=x^{2}+\quad x+ \\ \text { b) }(n-2)(n+7)=n^{2}+ \\ \text { c) }(r+12)(r-4)=r^{2}+ \\ \text { c) }\end{array} \)
Algebra Colombia Jan 22, 2025
The area of a rectangle is \( 28 \mathrm{ft}^{2} \), and the length of the rectangle is 1 ft more than twice the width. Find the dimensions of the rectangle.
Algebra United States Jan 22, 2025
If \( f(x)=x-5 \) and \( g(x)=x^{2} \), find \( (g \circ f)(x) \) \( x^{2}+5 \) \( x^{2}-5 x+25 \) \( x^{2}+25 \) \( x^{2}-25 \) \( x^{2}-10 x+25 \)
Algebra United States Jan 22, 2025

Latest Algebra Questions

If \( f(x)=x-5 \) and \( g(x)=x^{2} \), find \( (g \circ f)(x) \) \( x^{2}+5 \) \( x^{2}-5 x+25 \) \( x^{2}+25 \) \( x^{2}-25 \) \( x^{2}-10 x+25 \)
Algebra United States Jan 22, 2025
Solve: \( \begin{array}{l}\frac{6 x+18}{x^{2}}+\frac{1}{x}=\frac{3}{x} \\ \frac{19}{5} \\ \frac{1}{6} \\ \frac{13}{3} \\ -\frac{9}{2}\end{array} \)
Algebra United States Jan 22, 2025
Solving a word problem using a quadratic equation with rational roots The length of a rectangle is 3 yd less than twice the width, and the area of the rectangle is \( 27 \mathrm{yd}^{2} \). Find the dimensions of the rectangle. Length : Width : \( \square \mathrm{yd} \)
Algebra United States Jan 22, 2025
9) \( 5 x^{2}-16 x+3= \)
Algebra Mexico Jan 22, 2025
A function that converts dress sizes in the United States to those in Europe is given by \( D=f(x)=2 x+24 \) where \( x \) is the size in the United States. a. Find the European dress size that corresponds to a U.S. dress size of \( x=16 \). \( D=56 \) b. Find the function that converts European dress size to U.S. dress size. \( x=f^{-1}(D)=\frac{D-24}{2} \) c. Use part b. to find the U.S. dress size that corresponds to a Europen dress size 52 . \( x=14 \)
Algebra United States Jan 22, 2025
Prev Next
Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy