Form2 Maths!!!!

2012-02-21 5:08 am

(1) The value of a two-digit number is 3 times the sum of the two digits.If 9 is added to this two-digit number, the new value will be 4 times the sum of the two digits. Find the two-digit number.

(2) A boat takes 3 hours to reach a destination 48 km apart when it goes downstream and takes 4 hours for the return journey. What is the speed of the boat? What is the speed of the water current?

(3) Beer A contains 8% of alcohol by volume and beer B contains 3% of alcohol by volume. The brewer mixes beer A and beer B to produce a new beer that contains 5% of alcohol by volume. How much beer A and beer B should he mix to produce 1000mL of new beer respectively?

回答 (1)

[匿名]

2012-02-21 7:10 am

✔ 最佳答案

(1)
Let t be the ten digits, and u be the units digit.

10t + u = 3(t + u) ...... [1]
10t + u + 9 = 4(t + u) ...... [2]

[2] - [1] :
9 = t + u
u = 9 - t ...... [3]

Put [3] into [1] :
10t + 9 - t = 3(t + 9 - t)
9t + 9 = 27
9t = 18
t = 2

Put t = 2 into [3] :
u = 9 - 2
u = 7

Hence, the two-digit number = 27

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(2)
Let b km/hour be the speed of the boat, and w km/hour be the speed of the watercurrent.

3(b + w) = 48 ...... [1]
4(b - w) = 48 ...... [2]

From [2] :
b - w = 12
b = 12 + w ...... [3]

Put [3] into [1] :
3(12 + w + w) = 48
12 + 2w = 16
2w = 14
w = 2

Put w = 2 into [3] :
b = 12 + 2
b = 14

Hence, the speed of the boat = 14km/hour
and the speed of the water current = 2km/hour

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(3)
Let a mL be the volume of beer A, and b mL be the volume of beer B.

a(8%) + b(3%) = (a + b)(5%) ...... [1]
a + b = 1000 ...... [2]

From [1] :
8a + 3b = 5a + 5b
3a - 2b = 0
1.5a - b = 0 ...... [3]

[2] + [3] :
2.5a = 1000
a = 400

Put a = 400 into [2] :
400 + b = 1000
b = 600

Hence, volume of beer A = 400 mL
and volume of beer B = 600 mL

參考: Adam

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