A boat rental company offers two different rental packages. The first rental package costs $45, plus $29.50 per hour. The second rental package costs $90, plus $0.70 per hour. Which answer choice best approximates the number of rental hours at which the boating packages cost the same amount? 4.5 hr 1.6 hr 2.1 hr 128.6 hr

Based on the cost of the different rental packages, they will most likely be equal after 1.6 hours

The first rental package is $45 flat and $29.50 per hour. Assuming the number of hours is x, this could be represented by the equation:

= 45 + 29.50x

The second rental package can be represented as:

= 90 + 0.70x

To find out when they will be equal, equate both equations:

45 + 29.5x = 90 + 0.70x

29.5x - 0.70x = 90 - 45

28.8x = 45

x = 45 / 28.8

x = 1.56 hours

= 1.6 hours

In conclusion, the boating packages will be equal in 1.6 hours.

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1.6 hr

Step-by-step explanation:

1st rental package: y = 29.50x + 45

2nd rental package: y = 0.70x + 90

Set the equation equal to each other;

29.50x + 45 = 0.70x + 90

Subtract 0.70x from both sides;

28.8x + 45 = 90

Subtract 45 from both sides;

28.8x = 45

Divide both sides by 28.8

x = 1.5625 ≈ 1.6

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

x = 3 ± √(5+y)