Question

Seven stethoscopes and five endoscopes cost $450.42, whereas five stethoscopes and seven endoscopes cost $504.30. How much does one stethoscope cost?

Answer 1

SOLUTION

Given the question, the following are the solution steps to get the price of one stethoscope

Step 1: Write the mathematical representations of the statements.

$\begin{gathered} \text{let s represents stethoscopes and e represents endoscopes} \\ \text{First statement} \\ 7s+5e=450.42----equation\text{ 1} \\ \text{Second statement} \\ 5s+7e=504.30-----\text{equation 2} \end{gathered}$

Step 2: Find the values for s by solving the two equations simultaneously using elimination method.

$\begin{gathered} 7s+5e=450.42 \\ 5s+7e=504.30 \\ \text{ multiply equation 1 by 7 and equation 2 by 5},\text{ we have} \\ 49s+35e=3152.94----\text{equation 3} \\ 25s+35e=2521.50----\text{equation 4} \\ \text{Equation 3-Equation 4} \\ 24s=631.44 \\ s=\frac{631.44}{24}=26.31 \end{gathered}$

Since s represents stethoscope, the price of one stethoscope is $26.31.