One type of rowboat seats 3 people is 18 and the other seats 5 people is 35.
Given that,
Georgia is renting two kinds of rowboats for the campout.
One type of rowboat seats 3 people and the other seats 5 people.
if 53 people will be at the campout and she rents 13 boats,
We have to determine,
How many of each type of boat does she rent.
According to the question,
Let, rowboat seat boat be x,
and other types of seats are y.
The campout and she rents 13 boats,
[tex]x + y = 13[/tex]
Total number of people coming for campout = 53
One type of rowboat seats 3 people and the other seats 5 people.
[tex]3x + 5y = 53[/tex]
On solving both the equation,
[tex]x + y = 13\\\\3x + 5y = 53[/tex]
From equation 1,
[tex]x = 13- y[/tex]
Substitute the value of x in equation 2,
[tex]3(13-y) + 5y = 53\\\\39 -3y+ 5y = 53\\\\2y = 53- 39\\\\2y = 14\\\\y = \dfrac{14}{2}\\\\y = 7[/tex]
Substitute the value of y in equation 1,
[tex]x + 7 = 13\\\\x = 13-7\\\\x = 6[/tex]
Therefore, she rents one type of rowboat that seats 3 people = 3x = 3(6) = 18
And the other seats 5 people = 5y = 5(7) = 35
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