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Tim’s weekly pocket money is $13.50 more than Sam’s. Sam spends $17.70 more than Tim every week. Tim spends 5/11 of his pocket money every week. Sam saves 1/2 as much as Tim every week. How much money does Sam spend in a week?

 May 21, 2022
 #1
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Sam's weekly allowance==S
Tim's weekly allowance ==S + 13.50


5/11[S + 13.50]==what Tim spends every week
5/11[S + 13.50] + 17.70 ==what Sam spends every 
week.


6/11[S + 13.50]==2 * 3/55[10S - 437], solve for S


S==$100.90 - Sam's weekly allowance
$100.90 + $13.50 ==$114.40 Tim's weekly allowance.


$114.40 * 5/11 ==$52 - what Tim spends per week.
$52 + $17.70 ==$69.70 - what Sam spends per week


$100.90 - $69.70 ==$31.20 - what Sam saves per week.
$114.40 - $52 ==$62.40 - what Tim saves per week.

 May 21, 2022
 #2
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Let weekly pocket money of Tim = x

and Sam's weekly pocket money = y

According to question,

            x = y + 13.50 => y = x - 13.50

Tim spends = 5/11 * x ---- (1)

Sam spends = 5/11x + 17.70 ---- (2)

Total saving of Tim = x - 5x/11 = 6x/11

Sam's saving = 1/2 * 6x/11

Sam spends = Sam's weekly pocket money 

                               -- Sam's saving

5x/11 + 17.70 = y - (6x/(2 * 11))

5x/11 + 17.70 = (x - 13.50) - (6x/22)

5x/11 + 17.70 = x - 6x/22 - 13.50

5x/11 - x + 6x/22 = - 13.50 - 17.70

(10x - 22x + 6x)/22 = -31.20

6x/22 = 31.20

x = (31.20 * 22)/6

x = 114.4

Sam's weekly spend = 5x/11 + 17.70

                              = (5 * 114.4)/11 + 17.70

                              = 52 + 17.70

                              = $69.70

 May 22, 2022

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