The sum of two integers is 48. When twice the smaller integer is subtracted from the larger, the result is 12. find the integers.

Question

The sum of two integers is 48. When twice the smaller integer is subtracted from the larger, the result is 12. find the two integers.

 

Answer 1

Call the larger integer X and the smaller one Y. Then the problem can be expressed as follows:

 

 

X + Y = 48

 

X - 2Y = 12

 

 

Do you know how to solve those equations for X and Y?

 

If not, there are two equivalent approaches.

 

1. You can add (or subtract)  a multiple of one equation to (or from) the other to eliminate one of the variables (add 2X + 2Y = 96 from the second equation to get rid of Y, for instance).

 

2. Or solve one of the equations for X (for instance, from the first equation X = 48 - Y) and substitute that in the other equation:  48 - Y - 2Y = 12, or 48 - 3Y = 12, from which it follows that 3Y = 36 and Y = 12 and since X = 48 - Y,  X = 36.

 

Checking, 36 + 12 = 48, and 36 - 2*12 = 12.

 

Answer 2

First, let's focus in on what is meant by "the sum of two integers is 48" This is an algebra problem, so it involves unknown values. Let "x" represent the larger unknown and "y" as the smaller unknown.

In the problem, it says "the sum of two integers is 48" which means that together the unknowns equal 48: x+y=48.

 

"twice the smaller integer is subtracted from the larger" means that its x-2y since y is smaller than x and twice indicates 2. That equals 12 so the equation is x-2y=12

 

Now that you have both equations, solve for one of the unknowns first with substitution. Let's find y first. To do so we must isolate x from the other terms. In the first equation x+y=48 so if x is by itself, then x=48-y leaving only y terms when substituted into the other equation.

 

2y-x=12 so after substitution it becomes (48-y)-2x=12. In a sense you are distributing -1 in front of the quantity so now it becomes:

 

48-3y=12.

 

Combining like terms, 3y-48=12. Now to isolate the y, we must add both sides by 48 before we divide by 3:

 

-3y+48-48=12-48

3y=-36

-3y÷ -3= -36÷ -3

y=12

 

Now that y=12, we can solve for x. Knowing that x+y=48 and that y=12, solve for x with substitution:

 

x+12=48

x=48-12 which is 36

 

Check the math to see if it works for both equations: Does (12)+(36)=48?  Does (36)-2(12)=12? YES so the integers are 12 and 36