Twice the greater of two consecutive odd integers is 13 less than three times the lesser, how do you find the integers?

1 Answer
Aug 4, 2015

Answer:

The integers are #17# and #19#.

Explanation:

The trick when dealing with consecutive numbers of any kind is to use the smallest one to express the others.

In your case, if #x# is an odd number, the consecutive odd number will be #(x+2)#, since #(x+1)# would be an even number.

So, you know that if you double the bigger of the two numbers and add #13# to the result, you get a number that's three times larger than the smaller of the two numbers.

This is equivalent to saying that

#2 * underbrace((x+2))_(color(blue)("bigger number")) + 13 = 3 * underbrace(x)_(color(green)("smaller number"))#

This means that you have

#2(x+2) + 13 = 3x#

#2x + 4 + 13 = 3x => x = color(green)(17)#

The bigger number will be

#x+2 = 17 + 2 = color(green)(19)#