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?

2 Answers
Feb 12, 2018

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 = 50x+y=50

Equation 2 : 45x + 65y = 245045x+65y=2450

On solving the two equations, you get

x = 40x=40
y = 10y=10

Feb 12, 2018

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

Explanation:

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

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

x+y=50to(1)x+y=50(1)

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

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

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

"subtract term by term to eliminate x"subtract term by term to eliminate x

(2)-(3)(2)(3)

(0.45x-0.45x)+(0.65y-0.45y)=(24.5-22.5)(0.45x0.45x)+(0.65y0.45y)=(24.522.5)

rArr0.2y=2rArry=100.2y=2y=10

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

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

color(blue)"As a check"As a check

(2)to(0.45xx40)+(0.65xx10)=24.5 " correct"(2)(0.45×40)+(0.65×10)=24.5 correct