Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

14 hours

Step-by-step explanation:

20 + 4h = 14h

Joe's       y = 4x + 20  ($20 initial value and a rate of $4 per hr)

slope/rate is $4 per hour and the initial fee/y interceot is 20

Callie's    y = 14x (no initial fee and a flat rate if $14 per hr)

slope/rate is $14 per hour and the initial fee/y intercept is 0

Substitute in 3 for x to see who's price is better for 3 hours

y = 4(3) +20    or     y = 14(3)

y = $32                    y = $42

Callie's has the better deal for 3 hours. Only for 1 hour Joe has the better deal. At 2 hours, both are the same price, and 3 hours plus, Callie will always be cheaper.

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation:

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints