What two numbers have a sum of 319 and a difference of 57?

Answer 1

x + y = 319

x - y = 57

Add these two equations up by combining elements like-to-like:

x y 319

+ x -y 57

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2x = 376

Now we have an equation with just one variable. Divide each side by 2 to find the value of x.

2x 376

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2 2

x = 188

Now we know the value of x. Plug this value back into one of the original equations we created to find y.

x - y = 57

188 - y = 57

We want y alone on one side of the equation to find its value. Add +y to each side. On the left, -y and +y cancel out. On the right, we now have a +y.

188 = 57 + y

Now subtract 57 from each side, and we'll have the value of the second mystery number.

188 57 y

-57 -57

131 = y.

So, to answer: What two numbers have a sum of 319 and a difference of 57?

188 and 131!

Answer 2

We can write this as a system of two equations:

x + y = 319

x - y = 57

Adding the two equations together, we get:

2x = 376

And then we can solve for x by dividing both sides by 2:

x = 188

Finally, we plug this back into the second equation to solve for y:

188 - y = 57

y = 131

So the two numbers are 188 and 131!

Answer 3

Realizing that difference is the same as subtraction and sum is the same as addition, from the prompt we can determine two equations by assuming one number is called x and the other y.

x-y=57

x+y=319

One interesting thing to note is that we could also use the following two equations, and come to a similar answer.

y-x=57

x+y=319

Either way works. One core concept in math is the idea of unknown variables. In this case, we have two unknowns (x and y), and we have two equations. It's good to think of each unknown as a screw with a different head - only a certain screwdriver will fit into the screw. Every screw in this analogy would need to be "unscrewed", or none can be unscrewed. Each equation represents the screwdriver that matches the screw. So if we have 2 equations, and 2 unknowns we have two screws, and two screwdrivers. If we have 2 unknowns and only one equation, we can't solve for either unknown. If we have 2 unknowns and 3 equations, then it is likely that either one of the equations is incorrect, or 2 of the 3 equations are actually equivalent when simplified.

Back to our original question:

y-x=57

x+y=319

solve one of the equations for either x or y:

y=x+57

using this, plug it into x+y=319, so

x+y=319

x+x+57=319

2x+57=319

x=131

solving for y is easy

y=x+57

y=188

Try using x-y= 57 instead of y-x=57, and see what you get!