SOLUTION: Hi, I am a Distance Education student. I am having trouble figuring out how to set this problem up to solve it. Thank you for your help :) Problem: Lake Perris charges boaters d

Question 61553This question is from textbook Essential Algebra
: Hi, I am a Distance Education student. I am having trouble figuring out how to set this problem up to solve it. Thank you for your help :)
Problem: Lake Perris charges boaters different user fees depending on the horsepower (hp) rating of their engines. Zero-5 hp boaters are charged $5 per day, 6-50 hp $12, and over 50 hp $25 per day. If a total of 49 boaters used the lake on a certain day and paid $699 in fees, how many of each type boater used the lake, if there were ten more 6-50 hp boaters than zero-5 hp boaters? This question is from textbook Essential Algebra

Answer by asha(30) (Show Source): You can put this solution on YOUR website!
let there be x zero-5hp boaters
there will be
x+10 6-50hp boaters
let there be y boaters over 50hp
given x+x+10+y=49
2x + y =39 eqn.1
zero hp boaters are charged 5$,6-50 hp boaters are charged 12$ and over 50hp boaters are charged25$
the eqn. will be 5x+12(x+10)+25y=699
5x+12x+120+25y=699
17x+25y=699-120=579 eqn.2
multiply eqn.1 by 25, we get
50x +25y =39*25 =975 eqn.3
eqn.3-eqn.2 gives
33x=975-579 =396
x =396/33 =12
plugging x value in eqn,1 we get
24+y =39
y=39-24=15
there are 12 zero hp boaters,22, 6-50 hp boaters and 15 boaters over 50hp.
you can check the answers by plugging in the values in the equations.
good luck !!!
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