# 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?

i got 24 and 25.

(3/5 of 25) - (1/2 of 24) = 3

(n+1)*3/5 - 1/2 n =3 Right?

I will be happy to critique your thinking. I suggest start by multiplying each side by 10.

whoops, sorry bob

## No worries, Bob! Let's solve the equations step by step:

Considering the consecutive integers as n and n+1, the equation becomes:
(3/5)(n+1) - (1/2)n = 3

Now, let's simplify the equation by multiplying each term by 10 to get rid of the fractions:

10 * [(3/5)(n+1)] - 10 * [(1/2)n] = 10 * 3

Simplifying further:

(6/10)(n+1) - (5/10)n = 30/10

Reducing the fractions:

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

Now we can work with the equation. Let's distribute the 3/5:
(3/5)n + 3/5 - (1/2)n = 3

Combining like terms:
(3/5)n - (1/2)n + 3/5 = 3

To solve for n, we need to find a common denominator between 5 and 2, which is 10.
(6/10)n - (5/10)n + 3/5 = 3

Now we can add the fractions:
[(6n - 5n + 6)/10] = 3

Simplifying:
(n + 6)/10 = 3

To isolate n, we can multiply both sides by 10:
n + 6 = 30

Subtracting 6 from both sides:
n = 24

So, the two consecutive integers are 24 and 25, just like you initially thought! Great job, Bob!

## No problem! Let's go step-by-step to solve the problem correctly.

Let's represent the first integer as "n" and the next consecutive integer as "n+1."

According to the problem, "One half of one integer is subtracted from three fifths of the next consecutive integer, and the difference is 3." We can express this as an equation:

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

To eliminate the fractions, let's multiply each term by the common denominator, which is 10:

10 * [(3/5)*(n+1)] - 10 * [(1/2)*n] = 10 * 3

6(n+1) - 5n = 30

Now we can simplify the equation:

6n + 6 - 5n = 30

Combine like terms:

n + 6 = 30

Subtract 6 from both sides:

n = 30 - 6

n = 24

So the first integer is 24, and the next consecutive integer is 24+1 = 25. Therefore, the two integers are 24 and 25.

To solve this problem, we can set up an equation based on the given information.

Let the first integer be represented by "n", and the next consecutive integer be represented by "n + 1".

According to the problem, "One-half of one integer" is equal to (1/2)n, and "Three-fifths of the next consecutive integer" is equal to (3/5)(n + 1).

The difference between these two values is 3. So, we can set up the equation:

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

To make the equation easier to solve, we can begin by multiplying each term by 10 to eliminate the fractions and simplify the equation:

10*(3/5)(n + 1) - 10*(1/2)n = 10*3.

This simplifies to:

6(n + 1) - 5n = 30.

Distribute the 6:

6n + 6 - 5n = 30.

Combine like terms:

n + 6 = 30.

Isolate the variable by subtracting 6 from both sides:

n = 30 - 6.

n = 24.

So, the first integer is 24, and the next consecutive integer is 24 + 1 = 25.

Therefore, the two integers are 24 and 25.