Collins Barker
06/29/2024 · Senior High School

29 Calson sold 8 teddy bears and 8 toy horses for \( \$ 72 \). One teddy bear and one toy horse cost \( \$ 9 \). He made \( \$ 24 \) more from selling the teddy bears than from selling the toy horses. What is the cost of one teddy bear?

UpStudy ThothAI Solution

Tutor-Verified Answer

Step-by-step Solution

Let's denote the cost of one teddy bear as \( T \) and the cost of one toy horse as \( H \). From the given information, we have the following equations: 1. \( 8T + 8H = 72 \) (The total cost of selling 8 teddy bears and 8 toy horses is $72) 2. \( T + H = 9 \) (The cost of one teddy bear and one toy horse is $9) 3. \( 8T - 8H = 24 \) (He made $24 more from selling teddy bears than toy horses) We can solve these equations to find the cost of one teddy bear. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}8T+8H=72\\T+H=9\\8T-8H=24\end{array}\right.\) - step1: Rearrange the terms: \(\left\{ \begin{array}{l}8T+8H=72\\8T-8H=24\end{array}\right.\) - step2: Solve the equation: \(\left\{ \begin{array}{l}H=9-T\\8T-8H=24\end{array}\right.\) - step3: Substitute the value of \(H:\) \(8T-8\left(9-T\right)=24\) - step4: Simplify: \(16T-72=24\) - step5: Move the constant to the right side: \(16T=24+72\) - step6: Add the numbers: \(16T=96\) - step7: Divide both sides: \(\frac{16T}{16}=\frac{96}{16}\) - step8: Divide the numbers: \(T=6\) - step9: Substitute the value of \(T:\) \(H=9-6\) - step10: Simplify: \(H=3\) - step11: Calculate: \(\left\{ \begin{array}{l}H=3\\T=6\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}H=3\\T=6\end{array}\right.\) - step13: Rewrite: \(\left(H,T\right) = \left(3,6\right)\) The solution to the system of equations is \( H = 3 \) and \( T = 6 \). Therefore, the cost of one teddy bear is $6.

Quick Answer

The cost of one teddy bear is $6.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text

Enter your question here…

By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
📸 STUDY CAN BE A REAL STRUGGLE
Why Not UpStudy It?
Select your plan below
Premium

You can enjoy

  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to answer and
    solution
Basic
  • Limited Solutions