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Shkiper50 [21]
3 years ago
8

Alice and Bob each have a certain amount of money. If Alice receives $n$ dollars from Bob, then she will have $4$ times as much

money as Bob. If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?
Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
5 0

Answer: 31 : 9

Step-by-step explanation:

Assume the following:

Alice's amount = P

Bob's amount = Q

Amount received = n

If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.

P + n = 4(Q - n)

P + n = 4Q - 4n

P = 4Q - 4n - n

P = 4Q - 5n - - - - (1)

If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob

P - n = 3(Q + n)

P - n = 3Q + 3n

P = 3Q + 3n + n

P = 3Q + 4n - - - - - - (2)

Equating both equations - (1) and (2)

4Q - 5n = 3Q + 4n

4Q - 3Q = 4n + 5n

Q = 9n

Express P in terms of n, use either equation (1) or (2)

From equation 2:

P = 3Q + 4n

Substituting Q = 9n

P = 3(9n) + 4n

P = 27n + 4n

P = 31n

Alice's amount = P, Bob's = Q

Ratio = P:Q

31 : 9

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7. 49

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Step-by-step explanation:

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3 0
3 years ago
a 400 g of a liquid of density 1.6g/cm3 is made from mixing liquids of density 1.2g/cm3 and 1.8g/cm3 find the mass of the liquid
gogolik [260]

Answer:

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Step-by-step explanation:

Let the:

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Mass of 1.8g/cm³ of liquid = y

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x + y = 400........ Equation 1

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x = 400 - 266.67g

x = 133.33g

Therefore, the mass of the liquid of density 1.2g/cm³ is 133.33g

7 0
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