Question

The second number is five more than the first number. The sum of three times the first and double the second number is 30. Find the numbers.

Answer 1

x = 4 and y = 9

Explanation:

Let x and y be the two numbers. Also,

Let the first number be x and the second number be y.

Converting the word expressions to an equation we get:

y = x + 5

3x + 2y = 30

Only thing left is to substitute y = x + 5 into the second equation

3x + 2y = 30

3x + 2(x + 5) = 30 (substituting y as x + 5)

3x + 2x + 10 = 30 (multiplying by both x and 5)

5x = 30 - 10 (collecting like terms to one side)

5x = 20

`(5x)/(5) = (20)/(5)` (divide both sides by 5 to get the value of x)

x = 4

Now that we know the value of x, we can find y.

y = x + 5

y = 4 + 5

y = 9

If you want to make sure your answer is correct, substitute x and y into the equation.

3x + 2y = 30

3(4) + 2(9) = 30

12 + 18 = 30

30 = 30