Word problem
*.) find two numbers that differs by 5 and whose product is 50
*.) Find 2 consecutive numbers whose product is 156
1.) Let's solve for the two numbers that differ by 5 and whose product is 50.
Let the first number be x.
The second number will be x + 5.
We'll set up the equation:
x * (x + 5) = 50
Expanding the equation:
x^2 + 5x = 50
Rearranging the equation:
x^2 + 5x - 50 = 0
Now let's solve for x by factoring or using the quadratic formula.
Factoring the equation, we have:
(x + 10)(x - 5) = 0
Setting each factor to zero:
x + 10 = 0 or x - 5 = 0
Solving each equation separately:
x = -10 or x = 5
Therefore, the two numbers are:
-10 and -5
or
5 and 10
2.) Let's find two consecutive numbers whose product is 156.
Let the first number be x.
The second number will be x + 1 since they are consecutive.
We'll set up the equation:
x * (x + 1) = 156
Expanding the equation:
x^2 + x = 156
Rearranging the equation:
x^2 + x - 156 = 0
Now we can solve for x by factoring or using the quadratic formula.
Factoring the equation, we have:
(x - 12)(x + 13) = 0
Setting each factor to zero:
x - 12 = 0 or x + 13 = 0
Solving each equation separately:
x = 12 or x = -13
Therefore, the two consecutive numbers are:
12 and 13
or
-13 and -12