Question

Barney and Robin went shopping at H&M. The store was having a sale on all shirts and pants. Barney spent $70 on 3 shirts and 2 pairs of pants and Robin bought 1 shirt and 4 pairs of pants for $90. c) Algebraically solve using either the Substitution Method or the Elimination Method to solve the system of equations made up of your answers to parts a and b. Show your work.

Answer 1

Define the system of equations

`\begin{gathered} 3x+2y=70 \\ x+4y=90 \end{gathered}`

Where x is the price for a shirt and y is the price for a pair of pants

Solve using substitution method

`\begin{gathered} 3x+2y=70 \\ 3x=70-2y \\ x=(70-2y)/(3) \end{gathered}`
`\begin{gathered} x+4y=90 \\ (70-2y)/(3)+4y=90 \\ -(2y)/(3)+4y=90-(70)/(3) \\ (10)/(3)y=(200)/(3) \\ 10y=200 \\ y=(200)/(10) \\ y=20 \end{gathered}`

Find x

`\begin{gathered} x+4y=90 \\ x=90-4(20) \\ x=10 \end{gathered}`

A shirt costs $10 and a pair of pants costs $20