Question

33. Three consecutiveintegers exist such that fivetimes the first number isequal to one more than twicethe sum of the second andthird numbers.Which equation accuratelysolves for the integers?Let n represent the firstnumber.

Answer 1

5n=1+2(n+1+n+2)

Explanation:

Let the first number = n

Therefore, the three consecutive integers are n, n+1, and n+2.

• Five times the first number = 5n

One more than twice the sum of the second and third numbers.

• The sum of the second and third numbers = n+1+n+2

,

• Twice the sum of the second and third numbers = 2(n+1+n+2)

• One more than twice the sum of the second and third numbers = 1+2(n+1+n+2)

Therefore, the equation that accurately solves for the integers is:

`5n=1+2(n+1+n+2)`

The last option is correct.