Question

When an integer is subtracted from 5 times the next consecutive integer, the difference is 17. Find the value of the greater integer.

Answer 1

To find the greater integer, first represent the smaller integer as x and set up the equation 5(x + 1) - x = 17. Solve for x to find the smaller integer. Then add 1 to get the greater integer, which is 4.

Step-by-step explanation:

To solve the problem, let's denote the smaller integer as x. Hence, the next consecutive integer, which is the greater one, will be x + 1. The question tells us that when the smaller integer is subtracted from five times the greater one, the difference is 17. Mathematically, this can be expressed as:

5(x + 1) - x = 17

Let's solve this step by step:

1. Expand the multiplication: 5x + 5 - x = 17
2. Combine like terms: 4x + 5 = 17
3. Subtract 5 from both sides: 4x = 12
4. Divide both sides by 4: x = 3

Therefore, the smaller integer is 3. To find the greater integer, we add 1 to the smaller integer:

Greater Integer: 3 + 1 = 4

The value of the greater integer is 4.

Answer 2

4

Step-by-step explanation:

5(x + 1) -x = 17 Distribute the 5

5x + 5 - x = 17 Combine like terms

4x + 5 = 17 Subtract 5 from both sides

4x = 12 Divide both sides by 4

x = 3

Three is the smaller integer and 4 is the greater integer.