Question

Nathan buys a combination of 45 cents stamps and 65 cents stamps at the post office. If he spends exactly $24.50 on 50 stamps, how many of each type did he buy?

Answer 1

The number of 45 cent stamps is 40 and the number of 65 cent stamps is 10.

Explanation:

Let the no. of 45 cent stamps brought be x and the no. of 65 cent stamps brought be y.

Equation 1 : `x +y = 50`

Equation 2 : `45x + 65y = 2450`

On solving the two equations, you get

`x = 40`
`y = 10`

Answer 2

`40" 45 cent stamps and "10" 65 cent stamps"`

Explanation:

`"let x be the number of 45 cent stamps"`

`"and y be the number of 65 cent stamps"`

`x+y=50to(1)`

`0.45x+0.65y=24.5to(2)`

`"to eliminate x multiply "(1)" by 0.45"`

`(1)to0.45x+0.45y=22.5to(3)`

`"subtract term by term to eliminate x"`

`(2)-(3)`

`(0.45x-0.45x)+(0.65y-0.45y)=(24.5-22.5)`

`rArr0.2y=2rArry=10`

`"substitute "y=10" in "(1)`

`(1)tox+10=50rArrx=40`

`color(blue)"As a check"`

`(2)to(0.45xx40)+(0.65xx10)=24.5 " correct"`