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Nina has exactly enough money to purchase 6 widgets. If the cost of ea

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Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 11 Jun 2011, 00:23
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Question Stats:

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Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?

A. $22
B. $24
C. $30
D. $36
E. $40

how to solve this algebraically ? thanks
[Reveal] Spoiler: OA

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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 11 Jun 2011, 00:34
shrive555 wrote:
Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?

$22
$24
$30
$36
$40

how to solve this algebraically ? thanks


C its is.
Let price = X
(x-1.25)8 = 6X
X= 5
hence total money = 6*5 = 30
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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 11 Jun 2011, 03:37
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I usually do not take the equations route so I tried without forming an equation..
A Rs. 1.25 decrease in the price enables Nina to buy 2 more widgets. The 2 widgets (at new price) cost Rs. 7.5 (or Rs. 3.75 per widget).

So the earlier price is 3.75 + 1.25 = 5..and total money (6 x5) Rs 30..
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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 11 Jun 2011, 06:07
MONEY = 6 (COSToriginal)
MONEY = 8 (COSToriginal - 1.25)

6C = 8(C-1.25)
6C = 8C-10
2C = 10
C = 5

MONEY = 6 x (COSToriginal) = 6 x 5 = 30

Hence, (C)
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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 11 Jun 2011, 10:44
Quantity * Cost of each = Total Amount

1st equation x * 6 = y
2nd equation (x-1.25) * 8 = y

Solve for x, x= 5
Therefore y = 6*5 = $30
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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 11 Jun 2011, 10:52
let x be money nina has to buy 6 widgets.

=> price per widget = x/6

and this price per widget was reduced by 1.25 , by which she was able to buy 8 widgets.

=> x = ((x/6)- 1.25)*8

=> x =$30

Answer is C.
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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 02 Oct 2016, 11:12
I have a question. How to best distinguish when to do algreba vs. backsolving? I used backsolving but it was long and tedious.

Backsolving:

step1: organize the formulas and what the question is asking of you. it is saying that the same total will provide you different units ( 6 vs 8 units) if the PPU is decreased from x to x-1.25

PPU x Units = total Cost
Units = Total Cost/PPU => Units = x/PPU

Step 2. Select B = x = total cost = 24

24/PPU = 6 => PPU = 4
24/(4-1.25)=8? => 4-1.25 = 2.75*8 = 22 not equal 24 so B is out.

if B is not the answer, stop here to decide if we go higher or lower. It seems to me that I would need a higher number that multiplied by 8 will give me a higher total. so I decide to go higher. A and B are out.

Step 3. test D
36/PPU = 6 => PPU = 6
36/(6-1.25)=8? => 4.75*8 = 38 => 38 is not equal to 36.

This tells me that 36 is too high, I need something lower. If 36 is too high, then D and E are out. from the prior test we know that A and B are out too. By default C is the answer.

Algebraic way:

step 1: Using the stem you can rewrite the below and, very important, write what you will be looking to solve. In this case, you are looking for x and the you will multiple x times 6 in order to get the total. In other words, you are looking for x (6) = total.

$ total(t) = units x ppu(x)
t = 6(x)
t = 8(x-1.25)

step2: you can then pair the same formulas such as 6(x) = 8(x-1.25) in order to solve for x => x=5

step3: put it back to the original formula in order to find the total => x(6) = t => 5(6) = 30.
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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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New post 18 Oct 2016, 16:14
Simple equation set-up.

6x=y
8(x-1.25)=y

Set them equal to each other --> you'll find x=5 --> plug into top eqn & y =30 (aka amount of money individual has)
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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea [#permalink]

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Re: Nina has exactly enough money to purchase 6 widgets. If the cost of ea   [#permalink] 10 Apr 2018, 00:08
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