SOLUTION: when the lesser of two consecutive integers is added to 5 times the larger number, the result is 71. find the integers

Question 882983: when the lesser of two consecutive integers is added to 5 times the larger number, the result is 71. find the integers
Answer by Leaf W.(135) (Show Source): You can put this solution on YOUR website!
Hello!
***
Since the integers are consecutive, the second will be exactly one greater than the first. Thus, you can call the first (the lesser) integer x, and the second (larger) one x + 1.
***
Let us model the statement "when the lesser . . . is added to 5 times the larger number, the result is 71" with an equation. Let us figure each part out piece by piece:
"the lesser of two consecutive integers": x
"the larger number": x + 1
"5 times the larger number": 5(x + 1)
"when the lesser of two consecutive integers is added to 5 times the larger number": x + 5(x + 1)
"when the lesser of two consecutive integers is added to 5 times the larger number, the result is 71": x + 5(x + 1) = 71
Therefore, our equation to model this statement is x + 5(x + 1) = 71
***
Now we simply solve the equation.
x + 5(x + 1) = 71
Distribute the 5 through the (x + 1): x + 5x + 5 =71
Add like terms: 6x + 5 = 71
Subtract 5 from both sides: 6x = 66
Divide both sides by 6: x = 11
***
Thus, x, which represents the value of the lesser integer, is equal to 11. Since the greater integer is x + 1, it is equal to 12.
***
Therefore, the integers are 11 and 12.
Let me know if you need any further clarification! =)
RELATED QUESTIONS
when the lesser of two consecutive integers is added to three times the greater, the... (answered by dabanfield)

If five times the lesser of two consecutive integers is added to three times the greater, (answered by checkley77)

When the smaller of two consecutive integers is added to two times the larger, the result (answered by mananth)

When the smaller of two consecutive integers is added to two times the larger the result... (answered by ewatrrr)

When the smaller of two consecutive integers is added to two times the larger, the (answered by Boreal)

When the smaller of two consecutive integers is added to two times the larger, the result (answered by sophxmai)

when the smaller of two consecutive integers is added to three times the larger, the... (answered by Nate)

When the smaller of two consecutive integers is added to four times the larger, the... (answered by ewatrrr,jorel1380)

When the smaller of two consecutive integers is added to six times the larger, the result (answered by wilft1)