Question

The sum of two consecutive integers is 59. Write an equation that

models this situation and find the values of the two integers?

Answer 1

The equation that models the situation when the sum of two consecutives integers is 59:

x + (x+1) = 59.

The two integers are 28 and 29.

Explanation:

Integers are whole numbers, which do not have decimals. They can be negative, positive, or 0. To write an equation that models this situation, you have to denominate the first integer as x and the second as x + 1, since they have to be consecutive. Then you have to isolate the variable x.

Solving the equation, where x is the first integer (smaller) and (x + 1) is the second:

x + (x + 1) = 59

x + x + 1 = 59

2x = 59 -1

2x = 58

2x / 2 = 58 / 2

x = 28

The first integer is 28 and the second is (28+1) = 29

Answer 2

Let the smaller of the two numbers be x. Therefore the larger number is 1 bigger, x+1.


`x + (x + 1) = 59`
We can solve this equation for x, which will be one of our two numbers.

`2x + 1 = 59`

`2x = 58`

`x = 29`
Now that we've found x, we can find x + 1. In this case,
`x + 1 = 29 + 1 = 30`.
Therefore, the two numbers are 29 and 30.