Question

Solving a word problem involving a sum and another basic... The sum of two numbers is 58 . The smaller number is 12 less than the larger number. What are the numbers?

Answer 1

The two numbers are 23 and 35.

Explanation:

Let the two numbers be A and B, where A is the smaller number.

"The sum of two numbers is 58" can be written as

(1) A + B = 58

"The smaller number is 12 less than the larger number" can be written as (2) A = B - 12

We have two equations and two unknowns. We can use substitution to find the answers.

rewrite either equation so as to isolate one of the unknows. I'll pick A + B = 58.

A + B = 58

A = 58 - B

Now that we have a definition of A, let's use it in the second equation:

A = B - 12

58 - B = B - 12 [Substitute A with (58 - B)]

58 - B = B - 12

- 2B = - 70

B = 35

We can use this is equation 1 to find A:

A + B = 58

A + 35 = 58

A = 23

================

Check:

Is the sum 58? 35 + 23 = 58 YES

Is the smaller 12 less than the larger? 35 - 23 = 12 YES

The numbers check OK

Answer 2

23 and 35

Explanation:

Let the larger number be x.

Smaller number = x - 12

Sum = 58

x + ( x - 12 ) = 58

x + x - 12 = 58

2x - 12 = 58

2x = 58 + 12 = 70

x = 70 ÷ 2 = 35

Largest number (x) = 35

Smallest number (x-12) = 35 - 12 = 23

( you can always cross check if it's right. Sum of both numbers should be 58 and 23+35 = 58 so it's correct! )