SOLUTION: I am having to write an algebraic equation for each problem and solve it. I am not sure how to do percentages. Could you please help me to better understand what I am doing. 1.)

Question 407758: I am having to write an algebraic equation for each problem and solve it. I am not sure how to do percentages. Could you please help me to better understand what I am doing.
1.)In 2006, the number of Americans who wee members of a health club was 42.7 million. This was an increase of 106% from the number of health club members in 1990. How many Americans were health club members in 1990.
2.) Juanita and Carlos borrowed $4800 at a simple interest rate of 11% for a period of 2 years. What was the interest?
3.) David had $4000 invested for one-fourth of a year at a simple interest rate of 6.1%. How much interest did he earn.
4.) Tori invested $8000 in money market funds. Part was invested at 5% simple interest and the rest was invested at 7% simple interest. At the end of 1 year. Tori had earned $496 in interest. How much did she invest in each fund?
5.) The Clarke family went sailing on a lake. Their boat averaged 6 kilometers per hour. The Rourke family took their outboard runabout for a trip on the lake for the same amount of time. Their boat averaged 14 kilometers per hour. The Rourke family traveled 20 kilometers farther than the Clarke family. How many hours did each family spend on their boat trip.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
1.)In 2006, the number of Americans who wee members of a health club was 42.7 million. This was an increase of 106% from the number of health club members in 1990. How many Americans were health club members in 1990.
increase in members = 106%
let members in 1990 be x
increase will be 106/100 *x
x+106x/100 =42.7
lcd=100
100x+106x=100*42.7
206x=4270
/206
x=20.7 million
2.) Juanita and Carlos borrowed $4800 at a simple interest rate of 11% for a period of 2 years. What was the interest?
I= p*r*t
p=4800
r=11%=0.11
t=2
I=4800*0.11*2
interest = $1056
3.) David had $4000 invested for one-fourth of a year at a simple interest rate of 6.1%. How much interest did he earn.
p=4000
r=6.1%=0.061
t=1/4 year
I=4000*0.061*1/4
I = $61
4.) Tori invested $8000 in money market funds. Part was invested at 5% simple interest and the rest was invested at 7% simple interest. At the end of 1 year. Tori had earned $496 in interest. How much did she invest in each fund?
5.00% per annum ------------- x
7.00% per annum ------------ y
total investment $8000
Interest----- $496.00
...
x+y8000 ------------------------1
5.00%x +7.00%y =$496.00
Multiply by 100
5x+7y=$49,600.00 --------2

Multiply (1) by -5
we get

-5x-5y =-40000

Add this to (2)

2y=$9,600.00

divide by 2

y=$4,800.00 investment at 7.00%
Balance $3,200.00 investment at 5.00%

5.) The Clarke family went sailing on a lake. Their boat averaged 6 kilometers per hour. The Rourke family took their outboard runabout for a trip on the lake for the same amount of time. Their boat averaged 14 kilometers per hour. The Rourke family traveled 20 kilometers farther than the Clarke family. How many hours did each family spend on their boat trip.
let clarke family sail x km : speed = 6 km/h
rourke family = x+20 km: speed = 14km/h
..
time = d/s
the time they sailed is same
x/6 = (x+20)/14
cross multiply
6(x+20)=14x
6x+120=14x
14x-6x=120
8x=120
/8
x=15km clarke family
Rourke family 15+10=35 km
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