1.One quarter of the coins in a box are $5-coins, two-ninths are $2-coins and the rest $3-coins. The total value of the coins is $1600. Find the total number of coins in the box.
2.The amount Tim spends on entertainment each month is ⅔ of that of his sister, Mary.
a) If Tim spends $150 more and Mary spends $150 less each month, the Mary’s expenditure becomes ⅔of Tim’s. How much does each spend on entertainment each month?
b) Tim and Mary want to buy a bicycle and a TV game. The money needed is $140 less than twice of the amount they have planned for entertainment each month. If the price of the bicycle is 4/13 of that of the TV game, what is the price of the TV game?
F.1 Mathematics - Equations
2013-10-30 7:45 am
回答 (2)
2013-10-30 8:03 am
✔ 最佳答案
1. Let n be the total number of coins in the box.n/4 * 5 + 2n/9 * 2 + (1-1/4-2/9)n * 3 = 1600
5n/4 + 4n/9 + (19/36)n * 3 = 1600
5n/4 + 4n/9 + (19/12)n = 1600
(5/4 + 4/9 + 19/12)n = 1600
59n/18 = 1600
n = 488.1355932 (not an integer)
I suppose you typed something wrong!!!
2.
(a) Let $x be the amount Mary spends.
Then Tim spends $ 2x/3
x - 150 = (2/3) (2x/3 + 150)
x - 150 = 4x/9 + 100
5x/9 = 250
x = 450
2x/3 = 300
Mary spends $450 per month and Tim spends $300 per month.
(b) Let $y be the price of the TV game.
Then the price of the bicycle is $ 4y/13.
y + 4y/13 = 2*(450+300) - 140
17y/13 = 1360
y = 1040
The price of the TV game is $1040.
2013-10-30 14:47:48 補充：
對，發問者有時都會大意～
我最初作答的時候都想過，但不便改太多～
我可以加入補充回答～
謝謝你的意見～
2013-10-30 14:59:02 補充：
1. Let n be the total number of coins in the box.
[If $3 coins are $1 coins, then]
n/4 * 5 + 2n/9 * 2 + (1-1/4-2/9)n * 1 = 1600
5n/4 + 4n/9 + (1-1/4-2/9)n = 1600
5n/4 + 4n/9 + 19n/36 = 1600
20n/9 = 1600
n = 720
The total number of coins in the box is 720.
2013-10-30 8:15 pm
I think the rest coins are $1 coins (common sense, HK$ does not have $3-coins.)
So there are 720 coins
So there are 720 coins
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