You Are Buying 3 Shirts And 2 Pairs Of Pants. You Spend $300. Let X Represent, The Price Of The Shirt And Y Represent The Price Of The Pants. Write An

You are buying 3 shirts and 2 pairs of pants. You spend $300. Let x represent

the price of the shirt and y represent the price of the pants. Write an equation
that can be used to find the price of the shirts and pants.
Directions: Write the equation in both slope-intercept and standard form for each of the
scenarios below.
a. Standard Form:
b. Slope-Intercept Form:
c. If the shirts cost $20 each how much were each of the pants?
d. Using the Standard Form, identify the x-intercept of the graph and explain
how the x-intercept relates to the price of the pants and shirts.

 

Answer:

Price of shirt: x

Price of pants: y

Total Price: 300

A.) Standard Form Equation

3x + 2y = 300  

B.) Slope-intercept Form:

2y = -3x + 300

y = (-3x + 300)/2

y = -3x/2  +  150 ⇒  Slope-intercept form equation

Where:

m = -3/2

y-intercept (b) = 150

C. If the shirts cost $20 each how much were each of the pants?

Let x = 20:

Find the unit cost (y) of pair of pants using the slope-intercept form equation:

y = -3x/2 + 150

y = -3(20)/2 + 150

y = -30 + 150

y = 120  ⇒  Unit cost of pants

$120  ⇒  Unit Price of pants when the unit price of shirt is $20.

D.  Identify the x-intercept of the graph.

To find the x-intercept, set y=0 in Standard Form:

3x + 2y = 300

3x + 2(0) = 300

3x/3 = 300/3

x = 100

The x-intercept is 100 at Point (x,y) = (100, 0).

Since the slope (m) is negative at -3/2, then x is inversely proportional to y.

As x-value or unit price of shirt increases, the y-value or unit price of a pair of pants decreases and vice-versa.