Word Problems ...Algebra?

Question

I need help i dont understand it says.

Translate to an equation and solve

1) The product of three more than a number times two less than the number is fourteen. Find the numbers.

2) The sum of the squares of two consecutive odd positive integers in 202. Find the numbers.

3) The product of two consecutive even whole numbers is 288. Find the numbers

Answer 1

You have to learn how to translate English into "Mathese". The word :"product" (and often just the word "of") means multiplication. Any form of the verb "to be" (such as is, was, were, be, being, been, and so on) generally means an equals sign.

In your case:

1) Let x and y be the numbers. (I'm assuming that the second time the number is mentioned, you mean it to be a different number).

The product of (multiplication) three more (addition) than a numbers times two less (subtraction) than another number is (equals) fourteen.

(x + 3)(y - 2) = 14

2) Let x be one integer. If they are consecutive odd integers, then they differ by 2, so the other would be x + 2.

The sum (addition) of the squares (obvious) of two consecutive odd positive integers is (equals) 202.

x^2 + (x + 2)^2 = 202

That should give you enough to get the last one.

Answer 2

) The product of three more than a number times two less than the number is fourteen. Find the numbers.

(x+3)(x-2)=14 ;; x^2 + x -6=14 ;; x^2 +x -20= 0 ;l (x+5)(x-4)=0 so, x= -5 or x=4

2) The sum of the squares of two consecutive odd positive integers in 202. Find the numbers.

x^2 + (x+2)^2 = 202 2x^2 + 4x+ 4 =202 2x^2+ 4x -198 = 0; divide by 2 -> x^2 +2x -99 = 0 (x+11)(x-9)=0 x= -11 or x= 9 so: either -11, -9 or 9,11
3) The product of two consecutive even whole numbers is 288. Find the numbers
(x)(x+2)=288 ;; x^2 + 2x = 288 ;; x^2 +2x - 288 = 0 ;; (x+18)(x-16) = 0 x= -18 or x= 16 thus either -18 and -16 ; or 18 and 20

Answer 3

1) (x+3)(x-2)=14

2) x^2 + y^2 = 202, y= x+2 (because they are consecutive odd positive integers)
x^2 + (x+2)^2 = 202

3) x(y) = 288, y=x+2
x(x+2) = 288

You should be able to solve them from there

Answer 4

1.
3 more than a number= (x+3)
2 less than a number= (x-2)
Product of the two is 14> (x+3)(x-2)=14
Solve equasion

2.
Two consecutive odd positive integers= (x),(x+2)
Squared, then added= x^2+(x+2)^2
x^2+(x+2)^2

3.
Two consecutive even whole numbers= x, (x+2)
Product of the two (expanded)- x^2+2x
Full equasion- x^2+2x=288
Solve equasion

Answer 5

sounds like a difficulty for calculating territory (or section). you've L for length and W for width so: length equals Width + 2 length circumstances Width equals the realm (Width+2) -which by the way is the length- circumstances Witgh equals 100 and twenty that signifies that length circumstances Width equals 100 and twenty that signifies that the realm is 100 and twenty no longer particular what the little ^ signal ability so can no longer help you with that area... Width = -12 isn't a valid answer because width can't be a unfavorable decision Width equals 10 yards - that's the valid answer for width (that i believe you probably did not get at the same time as fixing the project) if Width is 10 yards, then length = Width + 2 = 12 yards with a view to educate that Width = 10 and Lenght - 12 you want to multiply them and note in the adventure that they equivalent 100 and twenty (the realm that's given above) 10*12=100 and twenty - that's the evidence that length and width were calculated wisely. wish i replaced into of help.