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Expert: - 2/10/2011


Question
1)Mrs lee is 36yrs old & her daughter is 10 years old. In hw may years time, will Mrs. Lee be 3 times as old as her daughter?

2)The cost of 3 pairs of socks and 2 pairs of shoes was $33. If each pair of shoes cost 4 times more than a pair of socks, how much does each pair of shoes cost?

3)The capacity of 3 similar packet drinks and 4 similar can drinks is 2070 ml.
The capacity of 4 such packet drinks and 2 such  can drinks is 1660 ml.
Find the capacity of one packet drink.

Answer
1) If Mrs Lee is 36 and her daughter is 10, in X years they will be 36+X and 10+X, respectively.
We want to know what X is for 36+X = 3(10+X).  That is the same as 36+X = 30+3X.
Subtracting X from both sides gives 36 = 30+2x.
Subtracting 30 from both sides gives 6 = 2x.
Dividing both sides by 2 gives the answer, so x = 3.

To check, in 3 years Mrs Lee will be 39 and her daughter will be 13, and 13*3 = 39.

2) It is known that 3 socks and 2 shoes cost $33.
It is also known that each shoe is 4 times more than a sock.
Letting A be the number of socks and B be the numbers of shoes, this gives 3A + 2B = 33.
We are given that B=4A, so multiplying by 2 gives 2B = 8A.
Putting this in gives 3A + 8A = 33, which says 11A = 33, or A = 3.
Since B=4A and the value of A is 3, B = 12.

3) This can be used to set up the equations
3x + 4y = 2070 and 4x + 2y = 1660.

Multiply the 2nd equation by 2, giving 8x + 4y = 3320.
Subtract the 1st from this and get 5x = 1250 since 8x-3x=5x, the y's cancel, and 3320-2070=1250.

Divide by 5 and get x = 250.
Since 4*250=1000, we have 1000 + 2y = 1660, so 2y = 660, and that says y = 330.

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