Answer :
The total costs are the same when a kayak is rented for 5 hours
How do we determine the hours that both have the same costs?
The hours that both shops have the same cost is determined by equating the total cost in shop A to the total cost in shop B, in short, we need to first of all , model the total cost in each shop based on the straight-line equation formula shown below since the total cost is made of fixed charge and variable charge
y=a+bx
y=total cost
a=fixed charge for each shop
b=hourly fee
x=number of hours
Shop A:
total cost=8+3x
Shop B:
total cost=3+4x
8+3x=3+4x
8-3=4x-3x
5=x
At 5 hours both Shops A and B would have the same cost
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The hours when the cost of renting the kayaks would be the same is 5 hours.
The total cost of renting a kayak is $23.
When would the total cost be equal?
The equation that can be used to represent the total cost of renting a kayak is a linear function. A linear equation is an equation whose graph is a straight line. A linear equation increases by a predetermined constant. An example of a linear equation is x + 2.
The form that the equation would be is:
Total cost = rental fee + (hourly fee x number of hours)
Total cost at Shop A = $8 + $3h
Total cost Shop B = $3 + $4h
Where h is the number of hours the kayak was rented.
When the total costs are equal, the two above equations would be equal.
$3 + $4h = $8 + $3h
Combine similar terms: $4h - $3h= $8 - $3
Add similar terms together: h = 5 hours
Total cost = $3 + $4(5)
$3 + $20 = $23
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