Question
The difference between two numbers is 5, and their sum is 19. Find the numbers.
The difference between two numbers is 5, and their sum is 19. Find the numbers.
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Koala Tutor
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Let's call the two numbers x and y. We are given two pieces of information:
1) The difference between the two numbers is 5:
x - y = 5
2) Their sum is 19:
x + y = 19
We can solve these equations using a method called elimination. By adding the two equations together, we can eliminate the variable y:
(x - y) + (x + y) = 5 + 19
2x = 24
x = 12
Now that we know the value of x, we can substitute it back into one of the original equations to find y:
x + y = 19
12 + y = 19
y = 7
Therefore, the two numbers are 12 and 7.
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