Algebra Homework Problems... Word Probs into Equations

LovePink

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So I'm needing some serious help on turning word problems into equations. Haha. Here's the questions, if you can just tell me the equations then that's all I would need. You only have to explain if you want to:

1. The side of one square is 3cm longer than the side of a second square, and the area of the second square is 51(cm squared) less than the area of the first square. Find the length of a side of the second square.

2. A rectangle is 2cm wider && 5cm longer then a certain square. The area of the rectangle is 38(cm squared) greater than that of the square. What are the dimensions of the rectangle ?

3. The difference of the squares of two consecutive positive even integers is 164. Find the integers.

4. The difference of the squares of two consecutive negative integers is 9. Find the integers.

5. The product of two consecutive positive odd integers is 38 less than the square of the greater integer. Find the integers.

6. The product of three consecutive integers is 22 less than the cube of the middle integer. Find the integers.

7. The height of a rectangular box is 2cm less than the width. The length of the box is 5cm greater than the width. The sum of the areas of the top && bottom of the box is is 98(cm squared) greater than the sum of the areas of the ends. Find the dimensions of the box.

8. A rectangular box is 4cm longer and 3 cm narrower than a certain cube. The rectangular box and the cube have equal heights and equal surface areas. Find the length and width of the rectangular box.

9. A rectangular picture is 3cm longer than it is wide. The picture is surrounded by a frame that is 2cm wide. The area of the picture && the frame together is 100(cm squared) greater than the area of the picture. Find the width of the picture.

To anyone who writes the equations: please don't combine like terms,I just need the actual equation. && also THANKYOU. Luv ya:)
 
So I'm needing some serious help on turning word problems into equations. Haha. Here's the questions, if you can just tell me the equations then that's all I would need. You only have to explain if you want to:

1. The side of one square is 3cm longer than the side of a second square, and the area of the second square is 51(cm squared) less than the area of the first square. Find the length of a side of the second square.
The first thing you need to do is assign names to things: let "x" be the length of the side of the first square and "y" be the length of the second square. "The side of one square is 3cm longer than the side of a second square" says that x= y+ 3. How would you write the area of the first square in terms of x? How would you write the area of the second square in terms of y? Now what equation does " area of the second square is 51(cm squared) less than the area of the first square" give you?

2. A rectangle is 2cm wider && 5cm longer then a certain square. The area of the rectangle is 38(cm squared) greater than that of the square. What are the dimensions of the rectangle ?
Pretty much the same as 1 except that how we have both width and length. If we call the width and length of the first rectangle "x" and "y", respectively, and the length of a side of the second square "L", what do "A rectangle is 2 cm wider than the square" tell you? What about "A rectangle is 5 cm longer than the square"? How would you write the area of the rectangle and the square? What equation do you get from "The area of the rectangle is 38(cm squared) greater than that of the square"?

3. The difference of the squares of two consecutive positive even integers is 164. Find the integers.
Call the first integer "n". The the next "consecutive even integer" is n+ 2. What is the difference of their squares?

4. The difference of the squares of two consecutive negative integers is 9. Find the integers.
Call the first integer "n". The next consectutive integer is n+ 1. What is the difference of the squares?
(Both (3) and (4) will give you quadratic equations which has two solutions. Use the fact that the integers in (3) are positive and those in (4) are negative to determine which are the correct solutions.

5. The product of two consecutive positive odd integers is 38 less than the square of the greater integer. Find the integers.
Call the first integer "n". The next consecutive odd integer is n+ 2. Their product is n(n+1) and that is "the square of the greater integer", (n+2)^2, minus 38.

6. The product of three consecutive integers is 22 less than the cube of the middle integer. Find the integers.
Call the first integer "n". The next two consecutive integers are n+1 and n+2. The product of the three is n(n+1)(n+2) and that must be (n+1)^3- 22.

7. The height of a rectangular box is 2cm less than the width. The length of the box is 5cm greater than the width. The sum of the areas of the top && bottom of the box is is 98(cm squared) greater than the sum of the areas of the ends. Find the dimensions of the box.
Call the width of the box "w". then the height is w- 2 and the length is w+ 4. The areas of the top and bottom are each w(w+4). There are four ends, two with area w(w+ 2) and two with area (w+4)(w+2).

8. A rectangular box is 4cm longer and 3 cm narrower than a certain cube. The rectangular box and the cube have equal heights and equal surface areas. Find the length and width of the rectangular box.
Call the length of a side of the cube "x". the length of the rectangular box is x+ 4 and its width is x- 3. The cube has 6 faces each with area x^2. The rectangular box has two faces with area x(x+ 4), two with area x(x- 3), and two with area (x+4)(x-3).

9. A rectangular picture is 3cm longer than it is wide. The picture is surrounded by a frame that is 2cm wide. The area of the picture && the frame together is 100(cm squared) greater than the area of the picture. Find the width of the picture.
Call the width of the picture "w". Its length is w+ 3 and so its area is w(w+3). The frame increases both length and width by 2cm on each side- its width is w+ 2+ 2= w+ 4 and its length is w+ 3+ 2+ 2= w+ 7. The are of "picture & frame together" is (w+ 4)(w+ 7). Since that is "100 cm squared greater than the area of the picture", (w+ 4)(w+ 7)= w(w+ 3)+ 100.

To anyone who writes the equations: please don't combine like terms,I just need the actual equation. && also THANKYOU. Luv ya:)

In future, don't post so many problems together. Hints that help you get one or two should also lead you to solve the others.
 
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