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express this algebraically

example 

the sum of x and y equals 3 more than z . Expressed algebraically= x + y = z + 3

Help! :(

1. simple interest is the product of "p" dollars, "r" percent interest, and "t" years.

2. the interest at 6% for "t" years on $100; on $200: on "p" dollars

3.how many dollars willl "f" square ft of tile flooring cost at "c" cents per square foot?

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3 Answers

To express things algebraically, you need to substitute the words with letters, numbers, and equations.

For #1: Product = multiplication. It wants you to express that simple interest equals "p" times "r" times "t". The answer is i=(p)(r)(t) or i=prt


For #2: This is taking the first equation one step further, now giving you some numbers in addition to variables. The "r" has been replaced with 6% (.06), and is asking for 3 different equations. Time is still unspecified, so that remains "t". The question is the interest, so all the equations need to be set to I=.

The answers are:
i=(100)(.06)(t)

i=(200)(.06)(t)

i=(p)(.06)(t)

For #3: This question is unrelated to the previous 2. It's asking the price of flooring tile. It wants "f" square feet, at "c" cents per piece. The cost of the tile can be determined by multiplying the number of pieces by the cost. The answer to this problem is thereby that the cost equals (f)(c) or fc.

Substituting something algebraically simply means replacing the words with parts of an equation.

for #1 : "The product of" tells you that the upcoming items are multiplied therefore, we know that the equation will include p*r*t. The statement says that "simple interest is the product of", in algebra, "is" usually means =. So, we get simple interest = p*r*t.

for # 2: We are just using the equation we just determined in #1 and applying it to an actual situation:

            the answers become : i = 100*(0.06)*t , i = 200*(0.06)*t, i = p*(0.06)*t

 

for # 3 : We are told the cost per square foot is c cents. We also know how many square feet are used, so the equation to find total cost becomes : Cost = c*f

 

The first part is totally correct, x + y = z + 3, awesome!

1. The formula for simple interest:
[ending amount] = [starting amount] * [Interest Rate] * [Time] 

2. When given an interest rate in percent form, you need to convert it to decimal, and then add 1 to it, so that you can use it in the above formula. So 6% = 6/100 = .06
Then add 1 to .06 to get 1.06. Use 1.06 for [Interest Rate]

2a.  after t years you will have ($100 * 1.06 * t ) 
2b. after t years you will have ($200 * 1.06 * t )
2c. after t years you will have ($p * 1.06 * t )

3. If you are told straight away the the room has F number of square feet that need to be tiled, and you know that it costs C cents PER SQUARE FOOT, then the total will just be F * C. Example, if you had 4 square feet, and it costs 50 cents for every square foot, then the total would be $2.00.