Question 955723
1.
let b = Bill's age
let j = Jack's age
:
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
:
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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