Question

Three competing hot dog food trucks entered a competition to sell the most hot dogs. That's My Dawg sold 100 less than three times as many as Hot Dog Heaven. Hot Cats? sold 25 more than twice as many as Hot Dog Heaven. How many hot dogs did each vendor sell if they had a combined total of 3,195 hot dogs sold?

Answer 1

Let

x ----> total hot dogs sold by My Dawg

y ----> total hot dogs sold by Hot Dog Heaven

z ----> total hot dogs sold by Hot Cats

so

x+y+z=3,195 ------> equation 1

x=3y-100 ----> equation 2

z=2y+25 ----> equation 3

Solve the system of equations

Substitute equation 2 and equation 3 in equation 1

(3y-100)+y+(2y+25)=3,195

solve fr y

6y-75=3,195

6y=3,195+75

6y=3,270

y=545

Find out the value of x

x=3y-100 -----> x=3(545)-100=1,535

Find out the value of z

z=2y+25 -----> z=2(545)+25=1,115

therefore

The answer is

My Dawg 1,535

Hot Dog Heaven 545

Hot Cats 1,115