A wallet costs 5/7 as much as a backpack and twice as much as a card case. If the total cost of the 3 items is $203 , how much more does the backpack cost compared to the card case ?
*Please show me your steps eg ,
52 + 35 = 87
Ans : 87 pencils
THANKS
2007-01-16 19:52:10 · 5 answers · asked by Dark A 1 in Science & Mathematics ➔ Mathematics
you just asked and i just answer this 10 minutes ago
i will copy --- hope you vote me as best answer both times please
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the wallet is the thing mention most often so let it be x
the wallet cost 5/7 as much as the backpack, so the backpack cost (7/5) * x (the reciprical of 5/7). The backpack cost twice as much as the cardcase so the cardcase cost 1/2 x (the reciprical of 2)
so the cost of the 3 items is the x (wallet) + (7/5)x (the backpack) + (1/2)x (the cardcase) = $203
x + (7/5)x + (1/2) x = 203
10 is the least common denomator
(10/10)x + 14/10(x) + (5/10)x = 203
29/10(x) = 203 which can be written as
29x/10 = 203
29x = 2030
x = 70
so the wallet costs 70
the backpack is (7/5) * x = (7/5) * 70 = 98
the cardcase is (1/2) * x = (1/2) * 70 = 35
2007-01-16 20:05:27 · answer #1 · answered by Bill F 6 · 0⤊ 0⤋
Let the cost of backpack be x dollars.
According to your specifications:
Cost of wallet + cost of backpack + cost of card case = $203;
We substitute symbols and figures from above
5/7 * x + x + 5/14 * x = 203, or multiplying by 14,
10x + 14x + 5x = 203 * 14
29x = 203 * 14
or x = 98, 5/14 * x = 35
Backpack costs $98, card case $ 35
Backpack costs (98-35) = $ 63 more than card case
2007-01-17 05:33:29 · answer #2 · answered by Paleologus 3 · 0⤊ 0⤋
W(wallet) = 5B(backpack)/7 = 2C(card case)
W = 5B/7 = 2C
W + 5B/7 + 2C = 203
5B/7 = 2C
5B/14 = C ; The backpack is 5/14 as much as the card case.
Now, since W = 2C
2C + 5B/7 + 2C = 203
5B/7 + 4C = 203 Divide by 2
5B/14 +2C = 203/2
Since, 5B/14 = C
C + 2C = 203/2
3C = 203/2
C = 203/6 = $33.83 for Card Case
5B/14 = $33.83
B = 14($33.83)/5 = $94.72 for Backpack, which is
$94.72 - $33.83 = $60.89 more.
2007-01-17 04:08:03 · answer #3 · answered by boombabybob 3 · 0⤊ 1⤋
price of backpack = x
price of card case = y
5/7 x = 2y
5x = 14y
or, x = 14/5 y
x + y + 2y = 203
x + 3y = 203
substuting the value of x
14/5 y +3y = 203
y(14/5 + 3) = 203
29/5 y = 203
or, y = 203*5/29
y = 1015/29
y = 35
Now, x=14/5 y
x = 14/5 * 35
x = 490/5
x = 98
difference= cost of backpack - cost of card case
= 98 - 35
= $63 :ANSWER
2007-01-17 04:05:18 · answer #4 · answered by arunima 2 · 0⤊ 1⤋
the answer is 63 as others have said.
to boombaby:
your 3rd line, W + 5B/7 + 2C = 203 is wrong, the information states , W + B + C =203.
2007-01-17 04:40:20 · answer #5 · answered by cp_exit_105 4 · 0⤊ 0⤋