the sum of two numbers is 48 and the larger number is 14 more than the smaller number. Write two equations and solve them to find the two numbers

Question

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S S S S S S S S S S S S  S S S 

Answer 1

Let x = larger number

Let y = smaller numer

 

(1) x + y = 48

(2) x = y + 14

 

Solving (1) for x: 

x = 48-y

Substituting this into (2) and solving for y:

48-y = y+14

48-2y = 14

-2y = -34

y = 17

x = 48-y = 31

So, the smaller number is 17 and the larger number is 31

 

 

Answer 2

This is mostly a challenge of turning words into a mathematical equation, and then simple algebra. We have two numbers we want to find, and one is larger than the other. So let's make variables. How about this?

 

L=large number

s= smaller number

 

Now we have two easily remember-able variables. So if we examine the first half of the problem,

The sum of two numbers is 48. Okay, so

 

L+s=48

Easy enough, right?

 

Second half, the larger number is 14 more than the smaller number.

so L is 14 more than s

so L=14+s

or put another way, L-14 = s

You can use either equation.

 

Then you just need to substitute one equation into the other, so you get an equation with only one unknown variable. When you find that number, substitute it back into an original equation to find the other number.

 

Tada! Now you have both L and s