MHB Solve for the Two Numbers: Sum 9, Difference 6

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To solve for the two numbers with a sum of 9 and a difference of 6, let x be the smaller number and express the larger number as x + 6. Setting up the equations, x + (x + 6) = 9 simplifies to 2x + 6 = 9. Solving this gives x = 1. Therefore, the two numbers are 1 and 8.
paulmdrdo1
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can you help me solve this just using one variable

the sum of two numbers is 9 and their difference is 6. what are the numbers?

thanks!
 
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paulmdrdo said:
the sum of two numbers is 9 and their difference is 6. what are the numbers?
Let $x$ be the smaller of the two numbers. Since the difference is 6, the other number is $x+6$. Now try writing the equation saying that the sum of these numbers is 9 and try solving it.
 
Alternatively:

$x + y = 9$
$x - y = 6$

The second equation tells us:

$x = y + 6$

So substitute that value for $x$ into the first equation, to get an equation in the single variable $y$.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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