The larger of the two numbers is 12 more than the smaller number. if the sum of the two numbers is 74, find the two numbers.

Your answer is "The largest number is 43 and the smaller number is 31".  :)

Step-by-step explanation:

Pick two numbers for variables, like a and b.

Let a be the greater number.

The largest of two numbers is 12 more than the smaller number translates to (the word "is" means equals sign)

a = 12 + b

They told you the sum of the two numbers is 74, and that translates to (sum means to add)

a + b = 74.

Now, solve for b, so you get

b = 74 - a.

Plug this back into the first equation of a = 12 + b and you get

a = 12 + (74 - a)

Now, solve for a

a = 86 - a

2a = 86

a - 43

Now, you need to answer the question asked and find b.  Well, look at your two original equations

a + b = 74

43 + b = 74

b = 31

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step-by-step explanation: