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Answer

Method 1 :

8 files + 8 key chains ——- 96
1 files + 1 key chains ——- 96/8 = 12
7 files + 1 key chain ——- (1/3) x (7 key chains + 1 file)
21 files + 3 key chains ——- 7 key chains + 1 file
20 files ——- 4 key chains
5 files ——- 1 key chains
1 file + 5 files = 6 files ——- 12
1 file ——- 12/6 = 2
1 key chain ——- 12 – 2 = 10 

Method 2 :

8 identical files + 8 identical key chains —— 96
7 identical files + 1 identical key chain ——- 96/4 = 24
1 identical file + 7 identical key chains ——- 24 x 3 = 72

7 identical file + 49 identical key chains ——- 72 x 7 = 504
49 – 1 = 48 key chains ——- 504 – 24 = 480
1 key chain ——- 480/48 = 10
or
8 identical files + 56 identical key chains ——- 72 x 8 = 576
56 – 8 = 48 identical key chains ——- 576 – 96 = 480
1 key chain ——- 480/48 = 10

Ans : $10.

Ans : $10.

0 Replies 1 Like ✔Accepted Answer

Cost of 1 file -> u

Cost of 1 keychain -> p

At first

Cost of Ashley’s items -> 8u

Cost of sister’s items -> 8p

Exchange 1 file for 1 keychain

After

Cost of Ashley’s items -> 7u + 1p

Cost of sister’s items -> 1u + 7p

Given: In the end, Ashley’s total cost is ⅓ of sister’s total cost

3(7u + 1p) = 1u + 7p

21u + 3p = 1u + 7p

4p = 20u

p = 5u

Given: total cost is $96

8u + 8p = 96

8u + 8(5u) = 96

48u = 96

u = 2

p = 5u = 10

Cost of one keychain -> $10

1 Reply 1 Like

Check

File -> $2 each

Keychain -> $10 each

  Ashley Sister Total
Cost at first 16 80 96
Exchange 1 file for 1 keychain -2, +10 +2, -10  
Cost in the end 24 72 96

24/72 = 1/3

Checked

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