Answer/Discussion to 1a

A rectangular garden has a width that is 8 feet less than twice the length.  Find the dimensions if the perimeter is 20 feet.

Make sure that you read the question carefully several times. 

We are looking for the length and width of the rectangle.  Since width can be written in terms of length, we will let

Width is 8 feet less than twice the length:

*Inv. of sub. 16 is add 16

*Inv. of mult. by 6 is div. by 6

If length is 6, then width, which is 8 feet less than twice the length, would have to be 4.  The perimeter of a rectangle with width of 4 feet and length of 6 feet is 20 feet.

FINAL ANSWER: 

(return to problem 1a)

Since we are looking for how long it would take you to travel, we can use the distance/rate formula:

The variables in this formula represent the following:

d = distance
r = rate
t = time

FINAL ANSWER: 

We are looking for the amount of 25% antifreeze and 50% antifreeze needed to get 40 liters of 30% antifreeze.

x = number of liters of the 25%.

Since the two mixtures together need to be 40 liters, then we can take the total (40) and subtract from it the "given" number of liters (x):

40 - x = number of liters of the 50%.

*Combine like terms

*Inv. of add. 2000 is sub. 2000
 

*Inv. of mult. by -25 is div. by -25

If you have 32 liters of 20% solution and 8 liters of 50% solution you do get 40 liters of 30% alcohol solution.

FINAL ANSWER:

We are looking for how much she invested in EACH account.

x = amount invested in 7%

Since the two accounts together need to be $20000, then we can take the total (20000) and subtract from it the "given" number in the 7% account (x):

20,000 - x = amount invested in 9%

Note that you could have reverse those, the problem would still work out the same.

*Combine like terms

*Inv. of add. 1800 is sub. 1800
 

*Inv. of mult. by -.02 is div. by -.02

If you take 7% of $5000 and add it to 9% of $15000 you do get $1700.

FINAL ANSWER: