Question

Applications using factoring: set up an algebraic equation and then solve the following problems. 1. an integer is 3 less than 5 times another. if the product of the two integers is 36, then find the integers.

Answer 1

To solve the problem, set up an algebraic equation using the given information. Solve the equation to find the values of the integers.

Step-by-step explanation:

To solve this problem, we can set up an algebraic equation based on the given information. Let's call the first integer x and the second integer y.

The first piece of information tells us that 'an integer is 3 less than 5 times another,' which can be written as x = 5y - 3.

The second piece of information tells us that 'the product of the two integers is 36,' which can be written as xy = 36.

Now, we can substitute the value of x from the first equation into the second equation: (5y - 3)y = 36.

Simplifying this equation, we get 5y^2 - 3y - 36 = 0.

We can solve this quadratic equation using factoring, the quadratic formula, or graphing. By factoring, we can rewrite the equation as (5y + 9)(y - 4) = 0.

This gives us two possible solutions: y = -9/5 or y = 4.

However, since we are looking for integers, the second solution y = 4 is the only valid one. Substituting this value back into the first equation, we can find x: x = 5(4) - 3 = 17.

So, the two integers are 4 and 17.