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?
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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.
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