Question

One number is two less than five times another. If their sum is increased by six, the result is twenty-

two. Find the numbers
The smaller of the numbers is
and the larger is

Answer 1

• smaller: 3
• larger: 13

Explanation:

You want two numbers such that the larger is 2 less than 5 times the smaller, and their sum is 22 after it has been increased by 6.

Setup

Let x represent the smaller number. Then the larger is (5x-2) and the relation with regard to the sum is ...

(x) +(5x -2) +6 = 22

Solution

6x = 18 . . . . . . . . . . . . subtract 4 and simplify

x = 3 . . . . . . . . . divide by 6

(5x -2) = 5·3 -2 = 13

The two numbers are 3 and 13.

Check

The sum of the two numbers is 3+13 = 16. When that is increased by 6, the result is 16+6 = 22, as required.

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