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?
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.
+237 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
