Question 472691: if one half of an integer is added to one fifth the next consecutive integers,the sum is 17.find the integers. Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Let's call the integer N. Then the next consecutive integer is one more than N or it is N+1.
.
Now you are told to add 1/2 of the integer N (which is N/2) to 1/5 of the next consecutive integer. And 1/5 of the next consecutive integer is (1/5)*(N+1). This sum is to equal 17. In equation form this relationship is:
.
.
Get rid of the denominators by multiplying all terms in this equation by 10, a common denominator of 2 and 5, to get:
.
.
Divide the integer in each denominator into the integer in the corresponding numerator and the equation becomes:
.
.
Do the distributed multiplication on the left side and the multiplication on the right side to get:
.
.
Add the two terms containing N:
.
.
Get rid of the 2 on the left side by subtracting 2 from both sides:
.
.
Solve for N by dividing both sides by 7:
.
.
Then if N is 24, the next consecutive integer is 25, and those are the two integers asked for in the problem ... namely 24 and 25.
.
Check: 1/2 of N is 12, and 1/5 of N+1 is 5. If you add those two integers together, you do get 17 as is specified in the problem.
.
Hope that helps you to understand this problem.
(