Easy Algebra Word Problem!?
The Total yearly health bill of all the people in Stanton Rd is $480,000.
180 Adults and 240 Children live on Stanton Road,.
The health costs for an adult are $1500 per year more than a child.
Calculate the yearly health cost for a child.
2) Karen is 4 years younger than her brother Roger. If their ages are multiplied together and 22 is added you can get 9 times Roger's age. Write an Equation and solve it to work out each person's age.
I admit this was from school, but it is not homework. Plus i have no idea how to work this out, i have a test soon, so plz help out.
Comments
i'll do one q for you.
1.
total bill = $ 480, 000
if the health costs for a child = $ x
health costs for an adult = x + 1500
for 180 Adults and 240 Children, it amounts to = 180 * (x+1500) + 240 x
but it is = $ 480000
so that
180 x + 270000 + 240 x = 480000
420 x = 480000 - 270000
= 210000
so x = 210000 / 420
= 500
hence
yearly health cost for a child = $ 500
Question 1 has already been solved. The solution for Q 2 is below:
Let the age of Karen is x
so the age of Roger is (x+4)
Multiplying their ages and adding 22 will be equal to 9 times the Roger's age
So x(x+4)+22=9(x+4)
or x²+4x+22=9x+36
or x²+4x-9x+22-36=0
or x²-5x-14=0
or x²-7x+2x-14=0
or x(x-7)+2(x-7)=0
or (x+2)(x-7)=0
Either x=-2 or x=7
Since age cannot be in negative so Karen's age is 7 years and the age of Roger is 11 years
let the yearly health cost for a child be x
for an adult it will be x+1500
480000 = 180(x+1500) + 240x
480000 = 180x + 270000 + 240x
480000 - 270000 = 420x
210000 = 420x
x = 500
let roger's age be x
karen's age will be x-4
x(x-4) + 22 = 9x
x^2 - 4x + 22 =9x
x^2 - 4x - 9x + 22 = 0
x^2 - 13x + 22 = 0
x^2 - 2x - 11x + 22 = 0
x(x-2) - 11(x-2) = 0
(x-11)(x-2)=0
x - 11 = 0 or x-2 = 0
x = 11 or 2 ----> roger's possible ages
karen is x-4 = 11-4 = 7
or 2-4 = -2 (this is not possible) so roger is 11 and karen is 7
1) total cost, T=cost of an adult, A * 180 + cost of a child, C * 240
A=1500 + C
T=(1500+C)*180 +C*240
480000=(1500+C)*180 +C*240
480000=270000+180C+240C
480000-270000=420C
210000=420C
dividing both sides by 420 gives
500=C
cost of total number of children=500*240
=$120000
you can prove this by finding the total cost for adult,
(1500+500)*180=360000
120000+360000=480000
2)Let Karen's age be K
let Roger's age be R
K=R-4...............................(1)
KR+22=9R.....................(2)
substitute (1) into (2)
(R-4)R+22=9R
R^2-4R+22=9R
R^2-4R-9R+22=0
R^2-13R+22=0
R^2-11R-2R+22=0
R(R-11)-2(R-11)=0
(R-2)(R-11)=0
R=2 or R=11
but R can't be 2 since Roger is 4 years older than Karen
So now let's substitute R=11 into (1)
K=R-4
=11-4
=7
Answer: Karen's age is 7 and Roger's age is 11
you can prove this by substituting these val into (2)
KR+22=9R
LHS: 7*11+22=77+22=99
RHS: 9*11=99
LHS=RHS
K = R - 4
K*R + 22 = 9*R
1) 480,000 = 180(1500+C)+240C = 270,000 + 420C
420C = 210,000
C = $500 per year
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