Answer:

8 and 15

Step-by-step explanation:

Given: The product of two positive numbers is 120 and one number is 7 more than the other.

Asked: What are the two positive numbers?

Solution:

Step 1: Translate the mathematical statements into working equations. Let x be the smaller number and let y be the larger number.

Statement 1: The product of two positive numbers is 120

Equation 1: x ( y) = 120

Statement 2: one number is 7 more than the other.

Equation 2: y =  x + 7

Step 2: Substitute equation two in equation one in terms of y. Simplify the resulting equation.

x ( y) = 120

x (  x + 7 ) = 120

= 120

 - 120 = 0

Step 3: Notice that we have derived a quadratic equation. Use the quadratic formula to solve for x.

x =

 - 120 = 0

where a = 1, b = 7 and c = -120

x =

x = 8 , -15

x = 8

Step 4: Substitute the resulting value of x to equation 2.

y =  x + 7

y = 8 +7

y = 15

Checking: Substitute the resulting values of x and y to equations 1 and 2 to check and verify the final answers.

Equation 1: x ( y) = 120

                  8 ( 15) = 120

                   120 = 120

Equation 2: y =  x + 7

                   15 = 8 + 7

                    15 = 15

Final answer: Therefore, the two positive numbers are 8 and 15.

To learn more about quadratic formula, click the link below:

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