SOLUTION: 1. the perimeter of a rectangle is 400cm. The length is 40cm longer than the width. find the length and width. 2. Jack is twice as old as lacy. In three years the sum of their a

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Question 949678: 1. the perimeter of a rectangle is 400cm. The length is 40cm longer than the width. find the length and width.
2. Jack is twice as old as lacy. In three years the sum of their ages will be 63. How old are they now?
3. The price of a swimming pool has been discounted 15%, the sale is 1000. find the original list price of the pol.
4. The product of two consecutive odd number is 14 more than the square of the smaller number, find the two numbers.
Answer by macston(5194) (Show Source):
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PROBLEM 1:
W=width; L=length=W+40cm; P=perimeter=2(L+W)=400cm
400cm=2(L+W) Divide each side by 2.
200cm=L+W Substitute for L
200cm=(W+40cm)+W Subtract 40cm from each side.
160cm=2W Divide each side by 2.
80cm=W ANSWER 1: The width is 80 cm.
L=w+40cm=80cm+40cm=120cm ANSWER 2: The length is 120 cm.
CHECK:
P=2(L+W)
400cm=2(120cm + 80cm)
400cm=2(200 cm)
400cm=400cm
PROBLEM 2:
L=Lacy's age; J=Jack's age=2L
If in 3 years the sum of their age will be 63, currently the sum is 57 (63-3years aging for each)
J+L=57 years Substitute for J
2L+L=57 years
3L=57 years Divide each side by 3.
L=19 years ANSWER 1: Lacy is 19 years old.
J=2L=2(19 yrs)=38yrs ANSWER 2: Jack is 38 years old.
CHECK:
(J+3 years)+(L+3 years)=63 years
38 yrs+3 yrs+19 yrs+3 yrs=63 yrs
63 yrs=63 yrs
PROBLEM 3:
The pool is 85% of original price (100%-15%) so
$1000/0.85=$1176.47 ANSWER: The original price was $1176.47.
PROBLEM 4:
S=smaller number; S+2=larger number

Subtract S^2 from each side.
2S=14 Divide each side by 2.
S=7 ANSWER 1: The smaller number is 7.
S+2=9 ANSWER 2: The larger number is 9.
CHECK
Product of the two is 14 more than square of the smaller
(7)(9)=(7)(7)+14
63=49+14
63=63