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Two numbers have a sum of 24, and 7 times the first number minus the second number is equal to 16. What is the smallest number?

I'm supposed to translate the word problem into a system of equations then solve. Please help!!
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2 Answers

Let x and y be the 2 numbers.
 
Solve this system of equations:
 
x + y = 24
7x - y = 16
 
Add the 2 equations and get
 
8x = 40
x = 40/8 = 5
 
y = 24 - 5 = 19
 
The 2 numbers are 5 and 19.  Test the answers.
 
 
Hi Niya,
 
Let's call the two numbers A and B. 
 
Now, lets' read the problem word for word and convert it to math symbols:
"The sum of the numbers is 24" which means
 
A + B = 24  (This is the first equation of your system)
 
Next, we read, "7 times the first number minus the second number is equal to 16" which means
7A - B = 16  (This is the second equation of your system)
 
 
If I take the first equation and solve it for B (which means get B by itself on one side), we see that
B = 24 - A
 
Let's use this expression for B and substitute it in for B in the second equation
7A - B = 16
7A - (24 - A) = 16     See the replacement!  :)
 
7A - 24 + A = 16      Distribute the negative on the left side)
 
8A - 24 = 16
 
8A = 16 + 24
 
8A = 40
 
A = 5
 
which means that B must be 19 since the two numbers have to add up to 24.
 
A is the smallest number!  A = 5
 
Hope this helps!  :)