Question

the sum of two numbers is 28. four times the lesser number is seven more than 3 times the greater number. find the numbers.

Answer 1

• lesser: 13
• greater: 15

Explanation:

You want two numbers that have a sum of 28 such that 4 times the lesser is 7 more than 3 times the greater.

Setup

Let the (lesser, greater) numbers be represented by (x, y).

x + y = 28 . . . . . . their sum is 28

4x -3y = 7 . . . . . . 4 times the lesser is 7 more than 3 times the greater

Solution

Using the first equation to write an expression for x, we have ...

x = 28 -y

Substituting this into the second equation gives ...

4(28 -y) -3y = 7

112 -7y = 7 . . . . . . . . simplify

105 = 7y . . . . . . . . . add 7y-7

15 = y . . . . . . . . . . . divide by 7

x = 28 -15 = 13

The lesser number is 13; the greater number is 15.

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Additional comment

4 times the lesser number is 4·13 = 52.

3 times the greater number is 3·15 = 45.

52 is 7 more than 45, as required.