SOLUTION: 1. The sum of two numbers is 24. One number is one third of the other. Find the number. 2. The length of a rectangle is 6m longer than its breadth. If the length and breadth are

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 1. The sum of two numbers is 24. One number is one third of the other. Find the number. 2. The length of a rectangle is 6m longer than its breadth. If the length and breadth are      Log On


   

Question 157674: 1. The sum of two numbers is 24. One number is one third of the other. Find the number.
2. The length of a rectangle is 6m longer than its breadth. If the length and breadth are of the ratio 6:5, find the number.
3. A father is older than his son by 32 years. 6 years ago the father was 17 times as lod as his son. How old are they now.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the numbers a and b
(1) a+%2B+b+=+24
(2) a+=+%281%2F3%29b
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From (1)
b+=+24+-+a
substituting in (2)
a+=+%281%2F3%29%2A%2824+-+a%29
a+=+8+-+%281%2F3%29a
Multiply both sides by 3
3a+=+24+-+a
4a+=+24
a+=+6
b+=+24+-+a
b+=+24+-+6
b+=+18
The numbers are 6 and 18
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Length = L
width = W
(1) L%2FW+=+6%2F5
Multiply both sides by W
L+=+%286%2F5%29W
Substitute this in
(2) L+=+W+%2B+6
%286%2F5%29W+=+W+%2B+6
Multiply both sides by 5
6W+=+5W+%2B+30
W+=+30
and, from (2)
L+=+30+%2B+6
L+=+36
The length is 36 and the width is 30
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Father's age now is F
Father's age 6 years ago is F+-+6
Son's age now is S
Son's age 6 years ago is S+-+6
It is given that
(1) F+=+S+%2B+32
and
F+-+6+=+17%2A%28S+-+6%29
F+-+6+=+17S+-+102
Using (1),
S+%2B+32+-+6+=+17S+-+102
16S+=+102+%2B+26
16S+=+128
S+=+8
and from (1)
F+=+S+%2B+32
F+=+8+%2B+32
F+=+40
The Father is 40 and the Son is 8
check:
F+-+6+=+17%2A%28S+-+6%29
40+-+6+=+17%2A2
34+=+34
OK