the sum of two numbers is 72 and one of them is five times the other;what are the two numbers

Question

the sum of three consecutive odd integers is 597.find the integers.

Answer 1

For Part 1 the answers are actually 12 and 60.

Thanks

Answer 2

Kohwai,

 

Part 1)

Let's refer to the smaller number as "n". n represents the first number. Since the second number of five times greater than n, the second number will be represented as 5n (5 times n). In order to determine the value of the two numbers, you must first determine the value of n. This is done by adding the two numbers together, n and 5n. It can be simplified as 6n, which the problem states is equal to 72. Divide 72 by 6n and you can solve for n.

 

n+5n=72

6n=72

n=(72/6)

n=12

 

Now that n has been solved, 5n can be determined. 5 times 12 equals 60. 

The numbers are 12 and 60. This should be double checked to make sure that it is correct.

12+60=72   Correct

60 is 5 times greater than 12   Correct

 

Part 2)

The sum of three consecutive odd integers is 597.

Once again, use n to represent the first integer. Since the integers are both consecutive and odd, the next two numbers can be represented as n+2 and n+4. The problem now becomes:

(n)+(n+2)+(n+4)=597

 

Simplify

3n+6=597

3n=591

n=197

 

Going back to what was decided earlier, that the integers are n, n+2, and n+4, the other two can now be determined.

 

The integers are 197, 199, and 201

 

Double Check

197, 199, 201 are consecutive odd integers. Correct

197+199+201=597   Correct