Mary has x bookmarks and Wilson has y bookmarks. They are exchanging
bookmarks. If Mary gives Wilson 8 bookmarks, the number of bookmarks of
Wilson is 3 times as many as that of Mary. If Wilson gives Mary 8 bookmarks,
they have the same number of bookmarks. Find x and y.
Simplify (5a3 – 4a) – (2a3 + 5a2 – 8) – (6a2 + 3a –2), and give the answer in descending order.
F.2 MATHS..
2008-08-14 5:54 am
回答 (4)
2008-08-14 6:11 am
2008-08-14 6:39 am
For the fisrt part,
If x = number of bookmarks held by Mary, and
y = number of bookmarks held by Wilson,
3(x - 8) = y + 8 ---------------------- Equation 1
x + 8 = y - 8 ------------------------Equation 2
By Equation 2, we get
x + 8 = y - 8
x = y - 8 - 8
x = y - 16 ------------------------Equation 3
Put Equation 3 into Equation 1, we get
3(x - 8) = y + 8
3 [(y - 16) - 8] = y + 8
3 [y - 24] = y + 8
3 y - 72 = y + 8
3 y - y = 8 + 72
2 y = 80
y = 40
Put y = 40 into Equation 3, we get
x = y - 16
x = 40 - 16
x = 24
For the second part,
(5a3 – 4a) – (2a3 + 5a2 – 8) – (6a2 + 3a –2)
= 5a3 – 4a – 2a3 - 5a2 + 8 – 6a2 - 3a + 2
= 5a3 - 2a3 - 5a2 - 6a2 - 4a - 3a + 8 + 2
= 3a3 - 11a2 - 7a + 10
If x = number of bookmarks held by Mary, and
y = number of bookmarks held by Wilson,
3(x - 8) = y + 8 ---------------------- Equation 1
x + 8 = y - 8 ------------------------Equation 2
By Equation 2, we get
x + 8 = y - 8
x = y - 8 - 8
x = y - 16 ------------------------Equation 3
Put Equation 3 into Equation 1, we get
3(x - 8) = y + 8
3 [(y - 16) - 8] = y + 8
3 [y - 24] = y + 8
3 y - 72 = y + 8
3 y - y = 8 + 72
2 y = 80
y = 40
Put y = 40 into Equation 3, we get
x = y - 16
x = 40 - 16
x = 24
For the second part,
(5a3 – 4a) – (2a3 + 5a2 – 8) – (6a2 + 3a –2)
= 5a3 – 4a – 2a3 - 5a2 + 8 – 6a2 - 3a + 2
= 5a3 - 2a3 - 5a2 - 6a2 - 4a - 3a + 8 + 2
= 3a3 - 11a2 - 7a + 10
參考: myself !!!!
2008-08-14 6:24 am
For the fisrt part,
If x = number of bookmarks held by Mary, and
y = number of bookmarks held by Wilson,
3(x - 8) = y + 8 ---------------------- Equation 1
x + 8 = y - 8 ------------------------Equation 2
By Equation 2, we get
x + 8 = y - 8
x = y - 8 - 8
x = y - 16 ------------------------Equation 3
Put Equation 3 into Equation 1, we get
3(x - 8) = y + 8
3 [(y - 16) - 8] = y + 8
3 [y - 24] = y + 8
3 y - 72 = y + 8
3 y - y = 8 + 72
2 y = 80
y = 40
Put y = 40 into Equation 3, we get
x = y - 16
x = 40 - 16
x = 24
For the second part,
(5a3 – 4a) – (2a3 + 5a2 – 8) – (6a2 + 3a –2)
= 5a3 – 4a – 2a3 - 5a2 + 8 – 6a2 - 3a + 2
= 5a3 - 2a3 - 5a2 - 6a2 - 4a - 3a + 8 + 2
= 3a3 - 11a2 - 7a + 10
If x = number of bookmarks held by Mary, and
y = number of bookmarks held by Wilson,
3(x - 8) = y + 8 ---------------------- Equation 1
x + 8 = y - 8 ------------------------Equation 2
By Equation 2, we get
x + 8 = y - 8
x = y - 8 - 8
x = y - 16 ------------------------Equation 3
Put Equation 3 into Equation 1, we get
3(x - 8) = y + 8
3 [(y - 16) - 8] = y + 8
3 [y - 24] = y + 8
3 y - 72 = y + 8
3 y - y = 8 + 72
2 y = 80
y = 40
Put y = 40 into Equation 3, we get
x = y - 16
x = 40 - 16
x = 24
For the second part,
(5a3 – 4a) – (2a3 + 5a2 – 8) – (6a2 + 3a –2)
= 5a3 – 4a – 2a3 - 5a2 + 8 – 6a2 - 3a + 2
= 5a3 - 2a3 - 5a2 - 6a2 - 4a - 3a + 8 + 2
= 3a3 - 11a2 - 7a + 10
2008-08-14 6:13 am
3(x -8) = y+8 -----------(1)
x +8 = y - 8
=> x = y - 16 ------------(2)
sub (2) into (1):
3[(y-16) - 8] = y+8
3y - 56 = y + 8
2y = 80
y = 40
x = 40-16 = 24
(5a^3 - 4a) - (2a^3 + 5a^2 - 8) -(6a^2 + 3a - 2)
= 10 - 7a - 11a^2 + 3a^3
x +8 = y - 8
=> x = y - 16 ------------(2)
sub (2) into (1):
3[(y-16) - 8] = y+8
3y - 56 = y + 8
2y = 80
y = 40
x = 40-16 = 24
(5a^3 - 4a) - (2a^3 + 5a^2 - 8) -(6a^2 + 3a - 2)
= 10 - 7a - 11a^2 + 3a^3
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