Question 157674
Call the numbers {{{a}}} and {{{b}}}
(1) {{{a + b = 24}}}
(2) {{{a = (1/3)b}}}
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From (1)
{{{b = 24 - a}}}
substituting in (2)
{{{a = (1/3)*(24 - a)}}}
{{{a = 8 - (1/3)a}}}
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/W = 6/5}}}
Multiply both sides by {{{W}}}
{{{L = (6/5)W}}}
Substitute this in  
(2) {{{L = W + 6}}}
{{{(6/5)W = W + 6}}}
Multiply both sides by {{{5}}}
{{{6W = 5W + 30}}}
{{{W = 30}}}
and, from (2)
{{{L = 30 + 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 + 32}}}
and
{{{F - 6 = 17*(S - 6)}}}
{{{F - 6 = 17S - 102}}}
Using (1),
{{{S + 32 - 6 = 17S - 102}}}
{{{16S = 102 + 26}}}
{{{16S = 128}}}
{{{S = 8}}}
and from (1)
{{{F = S + 32}}}
{{{F = 8 + 32}}}
{{{F = 40}}}
The Father is 40 and the Son is 8
check:
{{{F - 6 = 17*(S - 6)}}}
{{{40 - 6 = 17*2}}}
{{{34 = 34}}}
OK