algebraic Equations

[匿名]

2010-10-25 1:37 am

The amount Tim spends on entertainment each month is 2/3 of that of his sister, Mary.
(a) If Tim spends $150 more and Mary spends $150 less each month, then Mary's expenditure becomes 2/3 of Tin'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?

更新1:

Thank you for your answer. But I don't understand why the algebraic equation for Tim is (T=2/3*M) ?

更新2:

THANK YOU VERY MUCH.

回答 (1)

用戶22403

2010-10-25 2:05 am

✔ 最佳答案

(a)
Let T be Tim's entertainment and M be Mary's

T = (2/3)*M.......................(1)
M-150 = (2/3)*(T+150).......(2)

From (2),
3*(M-150) = 2*(T+150)
3M-3*150 = 2T+2*150
3M-2T = 2*150+3*150
3M-2T = 5*150
3M-2T = 750.....................(3)

Sub (1) into (3),
3M-2*(2/3)*M = 750
3*3M-2*2*M = 750*3
9M-4M = 2250
5M = 2250
M = 450

Then, T = (2/3)*450 = 300

Therefore Tim spends $300 on entertainment each month and Mary spends $450 each month.

(b)
Let B be the price of bicycle and G be the TV game

B = (4/13)*G................................(1)
B+G = (450+300)*2-140................(2)

Sub (1) into (2),
(4/13)*G + G = 750*2-140
4G + 13G = 13*1360
17G = 17680
G = 1040

Therefore the price of TV game is $1040

2010-10-25 11:14:58 補充：
2010-10-25 09:45:24 補充
Thank you for your answer. But I don't understand why the algebraic equation for Tim is (T=2/3*M) ?

題目一開始已說明
The amount Tim spends on entertainment each month is 2/3 of that of his sister, Mary.
==> 在娛樂上,TIM係MARY的三分二$$

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