cant understand this home work .please show me how to do it?

Question

1. in a certain candy store 3pounds of candy and 2 pounds of mints cost $10.80,and 1 pound of candy and 3 pounds of mints cost$5.35.find the cost per pound of candy and of mints.
2.the sum of $10,000 is invest part at 12%interest and part at 9%interest.the combined incomes from the two investments is $1,005.how much money is invested at each rate.
3.flying with the wind,a jey can travel2,800miles in 4 hours.flying againts the wind,the sames distance takes 6 hours.find the rate of the jet and of the wind.
4.half the perimeter of a building is 100feet.the lenght of the building is 20 feet more than the width.find the dimensions of the building

Answer 1

These are two variable, two equation problems. The gist here is to define variables and then figure out how they are related. Let's look at the first one:

c = candy
m = mints

From the problem,

3c + 2m = 10.80
c + 3m = 5.35

We can solve for c in the second equation, and then plug that in to the first one:

c = 5.35 - 3m

3c + 2m = 10.80
3(5.35 - 3m) + 2m = 10.80
16.05 - 9m + 2m = 10.80
16.05 - 7m = 10.80
5.25 = 7m
m = 0.75

c = 5.35 - 3m
c = 5.35 - 3(0.75)
c = 5.35 - 2.25
c = 3.10

So the candy costs $3.10/pound and the mints are $0.75/pound.

The rest are similar in nature. For the second one:

x = part of the $10,000
10000 - x = the other part (both should add up to $10,000)

0.12x + 0.09(10000 - x) = 1005
0.12x + 900 - 0.09x = 1005
0.03x = 105
x = 3500

So, $3,500 was invested at 12% and the other $6,500 was invested at 9%.

For the third:

w = windspeed
j = jet speed

4(j + w) = 2800
j + w = 700
j = 700 - w

6(j - w) = 2800
6(700 - w - w) = 2800
4200 - 12w = 2800
1400 = 12w
w = 117 mph

j = 700 - w
j = 700 - 117
j = 583 mph

Finally:

l = length
w = width

l + w = 100
l = w + 20

(w + 20) + w = 100
2w + 20 = 100
2w = 80
w = 40

l = w + 20
l = 40 + 20
l = 60