please, please help!!! you would be awesome if you did?

Question

I have tried really hard but can't figure these problems out:

1) A coin bank contains 30 coins, all dimes and quarters, worth $5.70. Write a system of linear equations to represent this situation. How many dimes and how many quarters are in the bank?

2) You have $25 to spend on picking 21 pounds of 3 different types of apples in an orchard. The empire apples cost $1.40 per pound, the red delicious apples cost $1.10 per pound, and the golden delicious cost $1.30 per pound. You want twice as many red delicious apples as the other two types combined. How many pounds of each type of apple should you buy?

3) solve for a: S= a(1-r^n)
--------------- (divided by)
1-r

If you could help I would appreciate it sooo much!!!

Answer 1

1. You can do this with 1 or 2 variables.
If D= number of dimes, 30-D=number of quarters. Then 10*D + (30-D)*25 = 570. Solve.

2. This is best done with 3 variables.
Let E,R and G be the three type apples (first letter). Then E+R+G=21 (weight)
1.4*E+1.1*R+1.3*G= 25 (cost)
2*(E+G)= R (red delicious preference)
Again solve.

3. This is the sum of a finite geometric series. To isolate "a", multiply both sides by the reciprocal of the coefficient of a, (1-r^n)/(1-r)

Answer 2

it is a be conscious that has been over used to the factor of being very almost meaningless. it is meant to point some thing that evokes concern and ask your self, like MT. ST. Helens erupting, not french fries or a pair of denims. even though it is a great question, dude.

Answer 3

The first answer would be:
12 dimes=1.20
18 quarters= 4.50