Word Problem help?

Question

If one-half of one integer is subtracted from three-fifths of the
next consecutive integer, the difference is 3. What are the two integers?
Can you please show me the work so I can do this next time and understand it. Thanks!!!!

Answer 1

24, 25

Here is how. One number is 'x', the next integer is 'x+1' so you put them in the problem:

If one-half of one integer (1/2)(x) is subtracted from three-fifths of the next consecutive integer (3/5)(x+1), the difference is 3. What are the two integers?

So: (3/5)(x+1)-(1/2)x=3
You multiply times ten to get rid of the denominators:
(30/5)(x+1)-(10/5)x=30
6(x+1)-5x=30
6x+6-5x=30
6x-5x=30-6
x=24
So one number is 24 and the other (x+1) is 25.

Answer 2

Heres the solution:
let x be the first integer, and x+1 be the next consecutive integer.
As the problem states, the equation becomes
> 3/5 (x+1) – 1/2 x=3
> 3/5 x+3/5-1/2 x=3
> 3/5 x-1/2 x=3-3/5
> (6x-5x)/10=(15-3)/5
> 1/10 x=12/5
> x=24 (the integer) and x+1=25 (the consecutive integer)

Proof equation:
> 3/5 (25) – 1/2 24=3
> 15-12=3
> 3=3
hence verified.

Enjoy

Answer 3

Let X equal the smaller integer.
Then 3/5 (X+1) - X/2 = 3
Explanation: X+1 is the next consecutive integer greater than X. X/2 is one half of the smaller integer. Soooooooooo
distribute: 3X/5 + 3/5 - X/2 = 3 then subtract 3/5 from each side so 3X/5 - X/2 = 2 2/5 so 3X/5 - X/2 = 12/5 then multiply each side by 5 so 3X - 5X/2 = 12 then multiply each side by 2 so 6X - 5X = 24 so X=24 ..... that's the smaller integer - so 25 is the larger one. All one really need solve for is the smaller integer - the larger one takes care of itself.
Check it out--------- one half of 24 = 12, if one subtracts that from 3/5 of 25 (the next consecutive integer) which is 15 the answer is THREE! Yeeeee-Haaaaah!

Answer 4

Let the first integer be x, let the next consecutive integer be (x + 1), then writing this in a formula would b:

(3/5)*(x + 1) - (1/2)*x = 3
(3/5)*x + 3/5 - (1/2)*x = 3
(3/5)*x - (1/2)*x + 3/5 = 3
(6/10)*x - (5/10)*x + 3/5 = 3
(1/10)*x + 3/5 = 3
(1/10)*x = 3 - 3/5
10 * (1/10)*x = (15/5 - 3/5)*10
x = (12/5)*10
x = 120/5
x = 24

and so x+1=25

Therefore the two integers are 24 and 25

Answer 5

Is the answer 24? It has been awhile but I think this is correct.
First setup the equation:
3/5(X+1) - 1/2(X) = 3

Now solve it:

First multiply 3/5 by (X+1) and you get:
3/5X + 3/5 - 1/2X = 3

Now get rid of 3/5 on the left side by subtracting it from both sides
(3/5X + 3/5 - 1/2X) -3/5 = 3 - 3/5

{Math Note: 3/1 - 3/5 = (15/5 - 3/5) or 12/5}

This is what you have left:
3/5x - 1/2x = 12/5

(Next factor out x)
X(3/5 - 1/2) = 12/5

{Math Note: doing the math 3/5 - 1/2 would equal 6/10 - 5 /10
or in other words it equals 1/10}

X(1/10) = 12/5
X = 12/5 x 10/1
X= 24

Hope this helps

Answer 6

let A be the integer you are looking for. Then you have (3/5) x (A+1) - (1/2 x A)=3. You then rearrange as 3/5A + 3/5 -1/2A = 3. Rearr. again to get 1/10A = 2-2/5, or 1/10A = 12/5. Then solve for A which is (12/5) / 1/10, or 12/5 x 10 = 24. Clear as mud eh?

Answer 7

If n= the interger, then n+1= the next consecutive integer.

Then (3/5)(n+1) - (1/2)(n) = 3

Multiply both sides by 5 to get rid of the first denominator:

3(n+1) - (5/2)(n) = 15

Multiply both sides by 2 to get rid of the second denominator:

6(n+1) -5n = 30

Distribute the 6:

6n + 6 - 5n = 30

Combine like terms:

n + 6 = 30

Solve for n:

n = 24 and n+1= 25

Answer 8

Consecutive integers b & c
3c/5 - b/2 = 3
c - b = 1, or
c = 1 + b
Substituting
3(1 + b)/5 - b/2 = 3
6(1 + b) - 5b = 30
6 + 6b - 5b = 30
b = 24
Thus, c = 25
Check,
3(25)/5 - 24/2 = 3
15 - 12 = 3

Answer 9

the integers are n & n+1
(n+1)*3/5-n/2=3 multiply both sides by 10
6(n+1)-5n=30 distribute 6
6n+6-5n=30 subtract 6 from each side
n=24
n+1=25

check
25*3/5-24/2=15-12=3

Answer 10

Let
n, n + 1 be the two integers.

(3/5)(n + 1) - (1/2)n = 3

Multiply thru by 10.

6(n + 1) - 5n = 30
6n + 6 - 5n = 30
n = 24
n + 1 = 25

The two numbers are 24 and 25.