Problem solving using algebra equations....?

Question

1) Angie needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain yhid by mixing some pure antifreeze with an appropriate amount of a 40% antifreeze solution. how many quarts of each should she use?

2) stating the solution to each inequality in interval notation
-3 < or = to x < or = to -1

3) corresponding inequality and solution set
(---|---]
0 1 2

4)1/6-1/3t >0

5) -3/5<1/5-2/15w<-1/3

Answer 1

1) I'm not sure what yhid means.

If you need 20 quarts of 50% antifreeze and assuming pure antifreeze is 100% then if you have p quarts of pure and q quartz of 40% then

p + q = 20 (20 total quartz)

100%p + 40%q = 50%20

p +.4q = 10

subtract the 2nd equation from the 1st

.6q = 10
q = 10/.6 = 16.67
p = 3.33

2) -3 <= x <= -1

This says that x is in the closed interval [-3,-1] The interval is closed on both sides since x is allowed to be equal to the end points.

3)

0
since x can equal the endpoint on the right but cannot equal the endpoint on the left.

4)

1/6 - 1/3t > 0

1/6 > 1/3t

1/2 > t or t < 1/2

5)

-3/5 < 1/5 - 2/15 w < -1/3

multiply everything by 15 - this keeps the inequalities in the same direction.

-3/5*15 < 1/5 * 15 - 2/15 * 15 w < -1/3 * 15

-9 < 3 - 2w < -5

-9 - 3 < 3 - 3 - 2w < -5 - 3
-12 < -2w < -8
-6 < -w < -4
6>w>4

Answer 2

1. 50%(20) = 100%x + 40%(20-x)
1000 = 100x + 800 - 40x
200 = 60x
x = 2 2/3 qt,
so 2 2/3 qt of 100%, 17 1/3 qt of 40%

2. x in [-3,-1]

3. 0 < x ≤ 2

4. 1/6 - (1/3)t > 0
1/6 > (1/3)t
1/2 > t

5. -3/5 < 1/5 - (2/15)w < -1/3
-4/5 < -(2/15)w < -8/15
8 < 4w < 12
2 < w < 3