More simultaneous equations

1. Oz Jeans has factories in Mydney and Selbourne. At the Mydney factory fixed costs are
$28 000 per month and the cost of producing each pair of jeans is $30. At the Selbourne
factory, fixed costs are $35 200 per month and each pair of jeans costs $24 to produce.During the next month Oz Jeans must manufacture 6000 pairs of jeans. Calculate the
production order for each factory, if the total manufacturing costs for each factory are to
be the same.

2. A tea wholesaler blends together three types of tea that normally sell for $10, $11 and $12
per kilogram so as to obtain 100 kilograms of tea worth $11.20 per kilogram. If the same
amounts of the two higher priced teas are used, calculate how much of each type must be
used in the blend.

any working out is much appreciated. Thanks in advance :)

1. Let m = mydney production and s = selbourne production

m + s = 6000

cost of production...
in mydney = 28000 + 30*m
in selbourne = 35200 + 24*s
these are to be equal, so

28000 + 30m = 35200 + 24s

from the first equation
m = 6000 - s
so
28000 + 30(6000 - s) = 35200 + 24s
28000 + 180000 - 30s = 35200 + 24s
172800 = 54s
s = 172800/54 = 3,200 (Selbourne production)
m = 6000 - s = 6000 - 3200 = 2,800 (Mydney production)

(check: 28000 + 2800*30 = 112000
35200 + 3200*24 = 112000)

2. Let x = amount of $10 tea and y = amount of $11 and $12 tea each

x + 2y = 100

(10x + 11y + 12y)/100 = 11.2

from the first equation
x = 100-2y

so
(10(100-2y) + 11y + 12y)/100 = 11.2
1000 - 20y + 11y + 12y = 1120
3y = 120
y = 120/3 = 40
x = 100-2y = 100 - 2*40 = 20

So he needs 20kg of the $10 tea and 40kg of each of the $11 and $12 teas.

(check: (20*10 + 11*40 + 12*40)/100 = 11.20)