# Algebra

Sean and David had some allowance in the ratio of 3:7. They shared some money to buy a bracelet for their cousin. The ratio of the amount paid by Sean to the amount paid by David was 1:2. If David was left with \$176 and Sean had spent 1/4 of his money, how much was the bracelet they bought?

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1. Allowance:
Sean gets 3x
David gets 7x

Shared amount for bracelet:
Sean gave y
David gave 2y

Dave was left with 176 ----> 7x - 2y = 176 , #1
Sean spent 1/4 of his money ----> 3x-y = (3/4)x
12x - 4y = 3x
9x - 4y = 0 , #2

#1 times 2 ----> 14x - 4y = 352
#2 leave it ----> 9x - 4y = 0
subtract them
5x = 352
x = 70.40

sub into #2:
9(70.4) - 4y = 0
y = 158.40

cost of bracelet = y + 2y = 3y = \$475.2

check my arithmetic

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2. let S = Sean’s allowance
d = David’s allowance

s/d = 3/7; s = 3d/7
spent on bracelet:
(Sean paid)/David paid = 1/2 = (1/4s)/(d - 176) = 0.25s/(d - 176)
Substitute s = 3d/7:
1/2 ≠ (0.25(3d/7))/(d - 176) = (3d (0.25))/(7(d - 176))
2(3d)(0.25) = 7(d - 176)
1.5d = 7d - 1232
= -1232/-5.5 ; d = \$224
s = 3d/7 = (3(224))/7 = \$96
spent on bracelet : Sean = 1/4 (96) = \$24
David = 224 - 176 = \$48
cost of bracelet = amount paid by Sean + amount paid by David
= \$24 + \$48 = \$72
The bracelet they bought cost \$72.

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