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?

Question

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?

Answer 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

Answer 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.

Answer 3

To find out how much the bracelet cost, we need to determine the total amount of money that Sean and David had together.

Let's assume that Sean had x dollars.

Since the ratio of their allowances is 3:7, we can set up the equation:

3/7 = x/176

To solve for x, we can cross-multiply:

7x = 3 * 176

7x = 528

x = 528/7

x = 76

So, Sean had $76.

Now, we know that Sean spent 1/4 of his money on the bracelet.

1/4 * $76 = $19

Sean spent $19 on the bracelet.

Since the ratio of the amount paid by Sean to the amount paid by David is 1:2, we can find out how much David paid.

Let's assume that David paid y dollars.

1/2 = y/176

To solve for y, we can cross-multiply:

2y = 1 * 176

2y = 176

y = 176/2

y = 88

So, David paid $88 for the bracelet.

To find out the total cost of the bracelet, we add the amounts spent by Sean and David:

$19 + $88 = $107

Therefore, the bracelet they bought cost $107.