Question 955723: 1.bill is 3 times as old as his kid brother jack.four years ago,he was 4years less than 5times jack's age at that time.How old are they?
2.the length of a rectangle is three times its width.if the length is decreassed by 20ft and the width increassed by 10ft the are is increassed by 200 find the dimension of the rectangle.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 1.
let b = Bill's age
let j = Jack's age
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write an equation for each statement
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bill is 3 times as old as his kid brother jack.
b = 3j
four years ago, he was 4 years less than 5 times jack's age at that time.
b - 4 = 5(j-4) - 4
b - 4 = 5j - 20 - 4
b = 5j - 20 - 4 + 4
b = 5j - 20
replace b with 3j, from the 1st statement
3j = 5j - 20
20 = 5j - 3j
20 = 2j
j = 10 yrs is Jack's age
then
3(10) = 30 yrs is Bill's age
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2.the length of a rectangle is three times its width.
L = 3W
A = L*W
if the length is decreased by 20ft and the width increased by 10ft the area is increased by 200.
(L-20) * (W+10) = LW + 200
FOIL
LW + 10L - 20W - 200 = LW + 200
LW - LW + 10L - 20W = 200 + 200
10L - 20W = 400
simplify, divide by 10
L - 2W = 40
Replace L with 3W, from the 1st statement
3W - 2W = 40
W = 40 ft is the original width
then
3(40) = 120 ft is original length
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