The sum of two numbers is 8and the sum of their squares is 34. What is the smaller number?

Step-by-step explanation:

let the numbers be x,y

x+y=8

y=8-x

x²+y²=34

x²+(8-x)²=34

x²+64+x²-16x=34

2x²-16x+64-34=0

2x²-16x+30=0

x²-8x+15=0

1×15=15

5+3=8

5×3=15

x²-(3+5)x+15=0

x²-3x-5x+15=0

x(x-3)-5(x-3)=0

(x-3)(x-5)=0

either x=3 or 5

if x=3,y=8-3=5

if x=5,y=8-5=3

in either cases numbers are 3,5

and smaller number is 3.

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x