Question

If x and y take only natural number values, find the number of (x,y) pairs satisfying the equation 2x+5y=100

Answer 1

2x+5y=100

first give x=0
so 5y=100
y=100/5 =20

give y=0
2x=100
x=100/2=50

remember 0 is not a natural number

so value of x>0 and x<50
and y>0 and y<20

remember both x and y are natural numbers

so ordered pairs include
x=5,
2*5+5y=100
10+5y=100
5y=100-10=90
y=90/5=18
(5,18)

x=10
2*10+5y=100
20+5y=100
5y=100-20=80
y=80/5=16
(10,16)

x=15
2*15+5y=100
30+5y=100
5y=100-30=70
y=70/5=14
(15,14)

x=20
2*40+5y=100
40+5y=100
5y=100-40=60
y=60/5=12
(20,12)

.
.
.
(25,10)
(30,8)
(35,6)
(40,4)
(45,2)

so ordered pairs include (5,18)(10,16)(15,14)(20,12)(25,10)(30,8)(35,6)(40,4)(45,2)
so 9 pairs are there