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Problem 1202

# The sum of two numbers is 24 ; one number is 3 more than twice the other. Find the numbers.

Expert verified
The two numbers are $$x = 17$$ and $$y = 7$$.
See the step by step solution

## Step 1: Define the variables and set up the equations

Let x be the first number and y be the second number. We are given the following information: 1. The sum of the two numbers is 24: $$x + y = 24$$ 2. One number is 3 more than twice the other: We can write this as: $$x = 2y + 3$$ Now we have a system of two linear equations with two variables: 1. $$x + y = 24$$ 2. $$x = 2y + 3$$

## Step 2: Solve the system of equations

To solve this system, we can use the substitution method. Since we are given that $$x = 2y + 3$$, we can substitute this expression for x in the first equation: $$(2y + 3) + y = 24$$ Now, we can solve for y: $$3y + 3 = 24$$ Subtract 3 from both sides: $$3y = 21$$ Now, divide by 3 to find the value of y: $$y = 7$$ Now that we have the value of y, we can find the value of x from the second equation: $$x = 2y + 3$$ Substitute the value of y: $$x = 2(7) + 3$$ Calculate x: $$x = 14 + 3$$ So, x = 17

## Step 3: State the answer

The two numbers are x = 17 and y = 7.

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