Translate to a system of equations and solve.

1. The sum of two numbers is 27. One number is 3 more than the other. Find the numbers.

Step-by-step explanation:

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12 and 15

Step-by-step explanation:

Let the numbers be called x and y. We know from the first sentence that:

x + y = 27.

From the second sentence we know that x + 3 = y. (In this problem it does not matter which is x and which is y.)

Substituting in x + 3 into the first equation, we have

x + x + 3 = 27

2x + 3 = 27

2x + 3 - 3 = 27 - 3

2x = 24

x = 12

y = x + 3 = 15

Check: does x + y = 27? Yes, 12 + 15 = 27