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=\frac{70-2y}{3} \end{gathered}$$\begin{gathered} x+4y=90 \\ \frac{70-2y}{3}+4y=90 \\ -\frac{2y}{3}+4y=90-\frac{70}{3} \\ \frac{10}{3}y=\frac{200}{3} \\ 10y=200 \\ y=\frac{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