word problems

[Newbill937]

The question is.....

The product of two consecutive intergers is 11 more than their sum. Find the intergers.

 

[Gene]

You should be able to do this. It is simple enough. The two consecutive integers are x and x+1. You know what a product is and what a sum is. Write the equation.

 

[Newbill937]

I know all that, but what I dont get is how to get the product to be 11 mor ethan the sum...that doesnt make sense to me....

 

[Gene]

Ok, I'll embarass you.
The product is x(x+1) = x²+x
The sum is x+(x+1) = 2x+1
11 more than that is 2x+12
x²+x = 2x+12
It's that easy. You can solve that, can't you?

 

[fbutlere]

Solving Area Problems, Consecutive Intergers, etc

1. A rectangle has a length of x + 2 and a width of x - 2, and has an area of 60 square units. Find the length and width of the rectangle.

2. The length of a rectangle is 8 inches more thab its width, if 4 inches are taken from the length and added to the width, the figure becomes a square with an area of 289 square inches. What are the dimensions of the original figure?

3. The area of a square is numerically 77 more than the perimeter. Find the length of the side.

4. The product of two consective intergers is 2 less than 2 times their sum. Find the intergers.

5. Find three consecutive intergers such that the sum of all three is 36 less than the product of the smaller two.

6. Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 12 miles, the distance between the cars was 4 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?


7. A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 feet. Find the length of the ladder if the length is 4 feet more than its distance from the wall.


Solve the problem. Round to the nearest tenth, if necessary.

8. If an object is propelled upward from ground level with an initial velocity of 80.2 feet per second, its height "h" is in feet "t" seconds later is given by the equation h = -16t(squared) + 80.2t. After how many seconds does the object hit the ground?

9. If an object is propelled upward from a height of 48 feet at an initial velocity of 96 feet per second, then its height after "t" seconds is given by the equation "h" -16t(squared) + 96t + 48, where "h" is in feet. After how many seconds will the object reach a height of 192 feet?

Sovle the problem

10. The table shows the population of a city over the past five years.

Year Population (in millions of people)
1993 65
1996 65.5
1997 67
1998 69
1999 71.3

We used this data to develop the quadratic equation y = .373x(square) + .165x + 65, which models the population of the city "y" in millions in the year "x", where x = 0 represents 1995, x = 1 represents 1996, and so on. Use the model to find the estimated population in the year 2002, 2005, and 2010.

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[happy]

Re: Solving Area Problems, Consecutive Intergers, etc

Don't post a list of problems. What have you done on these? You should post new problems in new threads.

 

[mowlick]

The question is.....

The product of two consecutive intergers is 11 more than their sum. Find the intergers.

The first integer is x

The second integer is x + 1

The product of the integers = x(x + 1) = x^2 + x

The sum of the integers = x + x + 1 = 2x + 1

The product of two consecutive intergers is 11 more than their sum

therefore

x^2 + x - 2x - 1 = 11

therefore

x^2 - x - 1 = 11

and

x^2 - x - 1 - 11 = 0 =

x^2 - x - 12 = 0 =

(x - 4)(x + 3) = 0

therefore

x - 4 = 0 and x = 4

or

x + 3 = 0 and x = -3

Therefore

the first integer = 4 and the next = 4 + 1 = 5

and/or

the first integer = -3 and the next = -3 + 1 = -2