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Geometry problem and Percentage

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Geometry problem and Percentage

by phoenix9801 » Wed Jun 16, 2010 3:26 am
I need some clarification of the 2 problems please. If you can explain step-by-step instruction I would greatly appreciate it. Be Simple...


1- If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?



2- A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefits costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?
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by kvcpk » Wed Jun 16, 2010 3:45 am
area of rectangle = l*w

new length= 1.2l since it increased by 20 percent

new width= 1.2w since it increased by 20 percent

so new area = 1.2l * 1.2w
= 1.44lw

original was lw
so increase percent = 44 percent.
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by amising6 » Wed Jun 16, 2010 4:10 am
1- If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?



2- A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefits costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?

1)area of rectangle =length * width
let length be l and width be W
area = l*w
length increased by 20 % so new length l+ 20%of l=1.2 l
width increased by 20 % so new width =1.2w
area= 1.2l*1.2 W=1.44 lw
so increased in area 1.44 lw -lw=.44lw
so % increae (.44lw/lw)*100=44 %

2)let pre 1993
salary=s
fringe benefit cost=f
employement cost s+f


in 1993 salary rose 3 %
new salary =1.03s
in 1993 Fringe benefit rose 5.5 % so new Fring benefit =1.055f

employment cost 1.03s+1.055F
now as given overall employment cost increased by 3.5%

1.03s+1.055f=1.035(s+f)
solving
1.03s+1.055f=1.035s+1.035f
0.02f=0.005s
20f=5s
4f=s
employement cost pre 1993-= s+f
=4f+f=5f
ringe-benefit costs =4f
ringe-benefit costs % 4f/5f*100=80%
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by phoenix9801 » Thu Jun 17, 2010 2:14 am
amising6 wrote:1- If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?



2- A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefits costs. If salary costs rose 3 percent and fringe-benefit costs rose 5.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993?

1)area of rectangle =length * width
let length be l and width be W
area = l*w
length increased by 20 % so new length l+ 20%of l=1.2 l
width increased by 20 % so new width =1.2w
area= 1.2l*1.2 W=1.44 lw
so increased in area 1.44 lw -lw=.44lw
so % increae (.44lw/lw)*100=44 %

2)let pre 1993
salary=s
fringe benefit cost=f
employement cost s+f


in 1993 salary rose 3 %
new salary =1.03s
in 1993 Fringe benefit rose 5.5 % so new Fring benefit =1.055f

employment cost 1.03s+1.055F
now as given overall employment cost increased by 3.5%

1.03s+1.055f=1.035(s+f)
solving
1.03s+1.055f=1.035s+1.035f
0.02f=0.005s
20f=5s
4f=s
employement cost pre 1993-= s+f
=4f+f=5f
ringe-benefit costs =4f
ringe-benefit costs % 4f/5f*100=80%

Thanks for the help, but there is something I am not clear about... would you please explain ?

How did you move from E= S + F then to E = 4F + F = 5F

What Happen to S to make the new equation E = 4F + F = 5F ??? (can you show me how you can up with this new equation??)

then you said F as a percent of E is F/E = F/5F = 1/5 = 20%

(In here I am not sure how you moved from E = 4F + F = 5F to new equation F/E = F/5F = 1/5 = 20% ??? )
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by amising6 » Thu Jun 17, 2010 2:51 am
1.03s+1.055f=1.035(s+f)
solving
1.03s+1.055f=1.035s+1.035f
0.02f=0.005s
20f=5s
4f=s
employement cost pre 1993-= s+f
=4f+f=5f
ringe-benefit costs =4f
ringe-benefit costs % 4f/5f*100=80%
we are solving this equation


let me explain
1.03s+1.055f=1.035s+1.035f
1.055f-1.035f=1.035s-1.03s (taking common term on same side)
we can say
0.02f=0.005s (multiplying by 1000 both side)
20f=5s dividing both side by 5
4f=s --------(equation 1)
so we can conclude value of 4f is equal to value of s

employement cost pre 1993-
salary + fringebenfit tax
=s+f
=4f+f=5f (since we know s= 4f derived in equation 1 earlier)
noe fringe benefit tax was f
so fringe benefit tax in percent =(fringe benefit tax/employement cost)*100
=(f/5f)*100
=20%
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