Which company should she use if she wants to minimize the cost?

Question

The red cab company charges $3.50 upon entry and an additional $1.25 per mile driven. The yellow cab company charges $5 upon entry and an additional $1.15 per mile driven. Use the graphing method, the substitution method, or the linear combination method to determine your response.

Answer 1

first, need to identify equations for the each cab company.

 

let X be the mile driven and Y be the fare cost

 

red cab cost:   Y= 1.25X + 3.50

 

yellow cab cost:   Y = 1.15X + 5

 

I like to use the combination method to eliminate one variable

 

multiply -1 to one of the equation so -1[  Y= 1.25X + 3.50 ] = -Y = -1.25X -3.50

 

combine (add) them and eliminate the Y value

 

-Y = -1.25X - 3.50

 Y =   1.15X + 5

-------------------------

0 = -0.1X  + 1.5

 

0.1X  = 1.5

 

X = 1.5/0.1 = 15

 

input X = 15 to the original equation(s) to find Y

 

 Y = 1.15(15) + 5 = 17.25 +5 = 22.25

 

Y= 1.25(15) + 3.50 = 18.75 + 3.5 = 22.25

 

X = 15 miles and Y = $ 22.25

 

these values represents the red and yellow cab companies will charge the same amount when going exact 15 miles.

 

What if X is under or over 15 miles?

 

if X = 10 (under 15 miles)

red cab cost:   Y= 1.2(10) + 3.50 = 12 + 3.50 = 15.50 (cheaper)

yellow cab cost:   Y = 1.15(10) + 5 = 11.50 + 5 = 16.50

 

You can test out the X when greater than 15 miles

 

Conclusion.

 

if under 15 miles, then use Red cab company. if over 15 miles, then use Yellow cab company