F.2 maths

1a) (m + n) - (m - n) = 7 - 3
2n = 4
n = 2(m + n) + (m - n) = 7 + 3
2m = 10
m = 5
b)Let 1/x = m , 1/y = n ,By a) :
1/x = 5 and 1/y = 2
x = 1/5 and y = 1/2 2a) Let there be C cookies and D dishes :If she puts 3 cookies in each dish and 11 cookies will be remained :
3D + 11 = C ... (1)When she puts 5 cookies in each dish and 3 dishes are empty :
5(D - 3) = C ... (2)Sub. (1) into (2) :5(D - 3) = 3D + 11
5D - 15 = 3D + 11
2D = 26
D = 13 Sub. into (1) :
3(13) + 11 = C
C = 50∴ There are 50 cookies and 13 dishes.
b)Let E extra dishes are needed :2(D + E) = C
2(13 + E) = 50
13 + E = 25
E = 12∴ 12 extra dishes are needed.

1a. m+n=7
m-n=3
m=7-n

sub m=7-n into m-n=3
(7-n)-n=3
7-3 = 2n
2 = n
sub 2= n into m+n = 7
m+(2)=7
m=5

1b. let m be 1/x and n be 1/y
m=7-n

1a. m+n=7
m-n=3
m=7-n
sub m=7-n into m-n=3
(7-n)-n=3
7-3 = 2n
2 = n
sub 2= n into m+n = 7
m+(2)=7
m=5

1/x = 5
x = 1/5

1/y =2
y = 1/2

2012-12-08 13:31:54 補充：
2a. let x be the number of cookies and y be the number of dishes
x-3y=11
5(y-3) = x

x-3y=11
x=11+3y

sub x=11+3y into 5(y-3) = x
5(y-3) = (11+3y)
5y-15 = 11+3y
2y = 26
y = 13

sub y = 13 into x-3y = 11
x- 3 (13) =11
x = 50

2012-12-08 13:33:05 補充：
2b. 50/2 = 25
25-13 = 12
12 extra dishes are needed.