Word Problems

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Caiis101

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Jan 10, 2009
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I was given a take home test and I am stuck on two word problems and I can
t seem to find similar examples in my text. I am not looking for the answers just a guide/tips on how to go about solving. I
m not sure how to start them. Any help is greatly appreciated -- thanks!

1. The Length of a rectangle is 4 cm greater than the width, and the area is 77 sq cm. Find the dimensions of the triangle

2. If Rena invests $7500 at 7% per year how much additional money must she invest at 12% to ensure that the interest she receives each year is 10% of the total investment?
 
I was given a take home test and I am stuck on two word problems and I can
t seem to find similar examples in my text. I am not looking for the answers just a guide/tips on how to go about solving. I
m not sure how to start them. Any help is greatly appreciated -- thanks!

1. The Length of a rectangle is 4 cm greater than the width, and the area is 77 sq cm. Find the dimensions of the triangle

2. If Rena invests $7500 at 7% per year how much additional money must she invest at 12% to ensure that the interest she receives each year is 10% of the total investment?
 
Caiis101 said:
I was given a take home test and I am stuck on two word problems and I can
t seem to find similar examples in my text. I am not looking for the answers just a guide/tips on how to go about solving. I
m not sure how to start them. Any help is greatly appreciated -- thanks!

1. The Length of a rectangle is 4 cm greater than the width, and the area is 77 sq cm. Find the dimensions of the triangle

Let the width = w and the length = w + 4.
Remember the area is length • width.

2. If Rena invests $7500 at 7% per year how much additional money must she invest at 12% to ensure that the interest she receives each year is 10% of the total investment?
Click to expand...

Let x = amount of money invested at 12%
Remember that interest I = prt, where p is the principal (amount invested), r is the rate (in this case 0.07 or 0.12) and that t is the time (in this case t = 1).
 
Caiis101 said:
I was given a take home test and I am stuck on two word problems and I can
t seem to find similar examples in my text. I am not looking for the answers just a guide/tips on how to go about solving. I
m not sure how to start them. Any help is greatly appreciated -- thanks!

1. The Length of a rectangle is 4 cm greater than the width, and the area is 77 sq cm. Find the dimensions of the triangle

2. If Rena invests $7500 at 7% per year how much additional money must she invest at 12% to ensure that the interest she receives each year is 10% of the total investment?
Click to expand...

1. Draw a sketch. Decide on whether you want the length or width of the rectangle to be the unknown and label it "x". If you labeled the width x, then decide what the length should be labeled and label it. This decision is made on the basis of the wording "Length of a rectangle is 4 cm greater than the width". If you decided to choose the length as x, then label the width accordingly. Now that you have the length and width expressed in terms of x, recall that the area of a rectangle is given by the formula Area = length times width. Now that you know the area and have the length and width expressed in terms of x, plug those things into the formula. Now solve the resulting equation for x. Then answer the question posed by the problem. Check your answer by seeing that the numerical answers you have fulfill the requirements of the stated problem.

2. Use the formula "Amount = Principle X Rate of interest X Time. In this case Time is 1 year. Also, one approach is to realize that the final amount is composed of the amount earned at 7% plus the amount earned at 12%.

If you need more help, show us what you have done so far.
 
Caiis101 said:
… The Length of a rectangle is 4 cm greater than the width, and the area is 77 sq cm. Find the dimensions of the triangle.
Click to expand...


You typed "triangle". Do you mean "rectangle", instead?

If you would like to find the dimensions of a rectangle whose area is 77 square centimeters and whose length is 4 centimeters longer than its width, then here is how to start.

You need to know the following IMPORTANT formula that relates the dimensions to the area:

Area = Length x Width

We use this formula to write an equation with the given area of 77 square units.

L * W = 77

We're also told that L is 4 centimeters longer than W.

This information allows us to relate the length and width.

L = W + 4

Since the expression W + 4 has the same value as the symbol L, we can replace the symbol L with the expression W + 4 anywhere we like.

We make this substitution in the equation written above for area because that gives us an equation that contains only one symbol.

(W + 4) * W = 77

Do you know how to solve this equation for W?

Once you do, you have the width of the rectangle.

Find the length by using the other equation.

L = W + 4

If you want more help with either of these two exercises, then please show whatever work you can do, so far.

 
I'm confused on #2, if I do PRT I get

7500 X .07 X 1 =525
7500 X .12 X 1 =900

those are the answers right? is their anything further to do.I have a multiple choice for my answer and none of those even added together are one of my choices.
 
>2. If Rena invests $7500 at 7% per year how much additional money must she invest at 12% to ensure that the interest she receives each year is 10% of the total investment?

>I'm confused on #2, if I do PRT I get

7500 X .07 X 1 =525
7500 X .12 X 1 =900

It doesn't say that you invest or get 12% of 7500.

Start by naming things.

1) Let x be the amount of additional money that must be invested at 12%.
2) x+7500 is the total investment.
3) 7500 X .07 = 525 is the amount earned on that portion of the investment.
4) x X .12 = .12x is the amount earned on the other portion of the investment.
5) 525 + .12x represents the total amount earned on the investment.

Now, we want that amount to be equal to 10% of the total investment.

Your equation becomes "total amount earned on the investment equals 10% of the total investment.
 
Caiis101 said:
I was given a take home test ....Any help is greatly appreciated -- thanks!

1. The Length of a rectangle is 4 cm greater than the width, and the area is 77 sq cm. Find the dimensions of the triangle

2. If Rena invests $7500 at 7% per year how much additional money must she invest at 12% to ensure that the interest she receives each year is 10% of the total investment?
Click to expand...

Are you allowed to seek help for take-home tests?
 
yea we are she even suggested we have someone take for it us if we wanted,i think shes giving them out as a grade booster for the semester


thankyou for the help!
 
briansnycutie said:
… she even suggested we have someone take [it for] us if we wanted, i think [she's] giving them out as a grade booster for the semester
Click to expand...


This sounds like pure crap, to me.

 
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