What number are we. A special pair are we. our sum is 100. our product is our sum times 24. What number are we?

Answer 1

the answer is 60 and 40. here is how to prove it.

x+y=100

x*y=100*24

simplify

x=100-y

x*y=2400

substitution

(100-y)*y=2400

distribute

100y-y2=2400

multiply by -1

y2-100y=-2400

add both sides by 2400

y2-100y+2400=0

simplify

(y-60)(y-40)=0

divide both sides by (y-60)

y-40=0

add both sides by 40

y = 40

go back to (y-60)(y-40)=0 and divide both sides by (y-40)

y-60=0

add 60 to both sides

y= 60

there are two y values. 60 and 40

now use substitution to find x using y = 60

x+y=100

x+60=100

subtract 60 from both sides

x=40

now substitute the other y value (40)

x+40=100

subtract 40 from both sides

x=60

we now have our 4 values. x=40 and 60, y=60 and 40.

the pair of numbers is (60,40)

now lets test if we are correct

first plug x and y into the first equation

x+y=100

60+40=100

100=100

now lets plug it into the second equation.

x*y=100*24

60*40=2400

2400=2400

we have proved the answer!