Question

The sum of two numbers is 29. The difference between 4 times the first number and the second number is 6. Find the two numbers.

Answer 1

the two numbers are x = 7.2 and y = 21.8.

Explanation:

Let's call the first number x and the second number y. We can set up two equations based on the information given:

x + y = 29 (equation 1)

4x - y = 6 (equation 2)

We can use these two equations to solve for x and y.

To do so, we can use the method of substitution. Solving equation 1 for x, we get:

x = 29 - y

We can then substitute this expression for x into equation 2:

4(29 - y) - y = 6

Simplifying and solving for y:

116 - 4y - y = 6

115 - 5y = 6

-5y = -109

y = 21.8

So one of the numbers is y = 21.8. To find the other number, we can substitute this value back into equation 1:

x + 21.8 = 29

x = 7.2

Therefore, the two numbers are x = 7.2 and y = 21.8.

Answer 2

Let's call the two numbers x and y.

From the problem statement, we know that:

x + y = 29 (Equation 1)

4x - y = 6 (Equation 2)

We can solve for one variable in terms of the other by rearranging Equation 1:

y = 29 - x

Substitute this expression for y in Equation 2 and solve for x:

4x - (29 - x) = 6

5x - 29 = 6

5x = 35

x = 7

Now that we know x = 7, we can use Equation 1 to solve for y:

x + y = 29

7 + y = 29

y = 22

Therefore, the two numbers are 7 and 22.