SOLUTION: 17. The product of two numbers is 10. One number is 3 more than the other number. a. What is the quadratic equation that models these numbers? b. Solve the quadratic e

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Question 1197668: 17. The product of two numbers is 10. One number is 3 more than the other number.
a. What is the quadratic equation that models these numbers?

b. Solve the quadratic equation from "a" to find the pairs of numbers
Answer by MathLover1(20850) About Me  (Show Source):
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let two nubbers be x and y
if the product of two numbers is 10 we have
xy=10.....eq1
if one number is 3 more than the other number we have
x=y%2B3........solve for y
y=x-3.......eq.2
a. What is the quadratic equation that models these numbers?
xy=10....eq1, substitute y from eq.2
x%28x-3%29=10
x%5E2-3x=10
x%5E2-3x-10=0

b. Solve the quadratic equation from "a" to find the pairs of numbers
x%5E2-3x-10=0....factor
x%5E2%2B2x-5x-10=0
%28x%5E2%2B2x%29-%285x%2B10%29=0
x%28x%2B2%29-5%28x%2B2%29=0
%28x+-+5%29+%28x+%2B+2%29+=+0
solutions:
%28x+-+5%29=+0=>x=5
+%28x+%2B+2%29+=+0=>x=-2
go to
y=x-3.......eq.2, substitute x
y=5-3 =>y=2
y=-2-3 =>y=-5
you have two pairs of numbers:
x=5,y=2
or
x=-2,y=-5