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
Kashish
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 = 50#

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

On solving the two equations, you get

#x = 40#
#y = 10#

Jim G.
Feb 12, 2018

#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"#

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