Question

(Please please I really need help!!!!!) 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 pants and Robin bought 1 shirt and 4 pairs of pants for $90. (assume there is not sales tax). a) Write an equation to describe the total spent by Barney in the terms of numbers of shirts and pants purchased. Let x be the price of the shirt and let y be the price of a pair of pants.b) Write an equation to describe the total spent by Robin in terms of numbers of shirts and pants purchased. Let x be the price of the shirt and let y be the price of a pair of pants. c) Algebraically solve using either Substitution Method or the Elimination Method to solve the system of equations made up of your answer to part A and B. Show your work. d) Use a graphing calculator such as Desmos to graph your equations in Parts A and B. What is the coordinate point where these two lines intersect? How does this compare to your response in part c? e) What does the solution to the system of equations you got represent in the given scenario? Be specific.

Answer 1

let

the price of shirt = x

the price of the pair of pants = y

a. An equation to represent the total amount Barney spent can be represented below

$3x+2y=70$

b. An equation to describe the total amount spent by Robin in terms of number of shirt and pants can be written below

$x+4y=90$

c. The equations formed can be solved below

$\begin{gathered} 3x+2y=70 \\ x+4y=90 \\ x=90-4y \\ 3(90-4y)+2y=70 \\ 270-12y+2y=70 \\ 270-10y=70 \\ 270-70=10y \\ 200=10y \\ y=\frac{200}{10} \\ y=20 \\ \\ 3x+2y=70 \\ 3x+2(20)=70 \\ 3x+40=70 \\ 3x=70-40 \\ 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}$

d.

The co ordinates point where the two lines intersect is (10, 20) . It intersected point is the same with the x and y value when we solve the equation by using substitution method.

e. This means the price of each shirt is equals to $10 while the price of each pant is $20.