Question

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

Answer 1

Hi there!

Let th' two number be ' a ' and ' b ' [ a > b ]

According to th' question :-

→ The largest of two numbers is 12 more than the smaller number.

a = 12 + b ---(i)

→ Sum of the two numbers is 74.

a + b = 74

b = 74 - a ---(ii)

Substitute th' value of ' b in Eqn. :-

a = 12 + (74 - a)

a = 86 - a

a + a = 86

2a = 86

a = $\dfrac {86}{2}$ = 43

Now,
Substitute th' value of ' a ' in Eqn. (ii)

b = 74 - b

b = 74 - 43

b = 31

Hence,
The required answer is :-

• The smaller number is 31
• The largest number is 43

~ Hope it helps!

Answer 2

You can set up to solve this problem by creating 2 equations
x= larger number
y= smaller number

x = 12 + y (larger # = 12 more than the smaller #)
74 = x + y( the sum of the two numbers is 74)

you can use more than one method to go about solving this but I'm going to eliminate one of the variables


to do this, I am going to multiply the first equation by -1

-1(x = 12 + y)
-x = -12 - y

now you add the two equations together so that the -y and y cancel out

-x = -12 -y
74 = x + y

once added the sum will be 

74 - x = -12 + x

now solve for x

74 = -12 + 2x
86 = 2x
x = 43 

the larger number is x (43) so now you can plug in x into either equation and solve for y

43 + y = 74
y = 31 
31 is the smaller number

to make sure this is correct you can plug both numbers into the eqations
43 + 31 = 74
31 + 12 = 43

hope this helped!