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
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 :
Equation 2 :
On solving the two equations, you get
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)(0.45x−0.45x)+(0.65y−0.45y)=(24.5−22.5)
rArr0.2y=2rArry=10⇒0.2y=2⇒y=10
"substitute "y=10" in "(1)substitute y=10 in (1)
(1)tox+10=50rArrx=40(1)→x+10=50⇒x=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