SOLUTION: a stamp collection consist of 5, 13, and 18 cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. the number of 18 cent stamps is five more

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Question 49308: a stamp collection consist of 5, 13, and 18 cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. the number of 18 cent stamps is five more than the number of 13 cent stamps. the total value of all the stamps is $2.60. find the number of 13 cent stamps in collection.
Found 2 solutions by Osran_Shri, venugopalramana:
Answer by Osran_Shri(18) About Me  (Show Source):
You can put this solution on YOUR website!
Let us put the problem statement into Equation:
Let:
Number of 5 Cents Stamps = A
Number of 13 Cents Stamps = B
Number of 18 Cents stamps = C
Now:
Number of 13 Cents Stamps = B = (2A-1) The number of 13 cent stamps is one less than twice the number of 5 cent.
Number of 18 Cents stamps = C = B+5 = 2A-1+5 = 2A+4 :The number of 18 cent stamps is five more than the number of 13 cent stamps. Note that I have converted interms of " A".
We know that : 5A + 13B + 18C = $2.6 = 260 Cents
In the above equation, substitute the values interms of "A" to get following equation.
5A + 13(2A-1) + 18( 2A+4) = 260
5A+26A-13+36A+72 = 260
67A-13+72 = 260
67A = 260+13-72 = 201
A = 201 / 67 = 3
Therefore B = 2A-1 = 2*3-1 = 5
Hence Number of 13 Cents stamps = B = 5
Also C= 2A + 4 = 2*3+4 = 10
Answers : A=3, B=5, C=10 We can verify the answers by substituting values in the following equation:
5A + 13B + 18C = 260 Cents
5*3 + 13*5 + 18*10 = 15+65+180 = 260
Thats all.....
B.Shridhar





Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
a stamp collection consist of 5 (F NUMBERS SAY), 13(T), and 18(E) cent stamps. The number of 13 cent stamps is one less than twice the number of 5 cent stamps. the number of 18 cent stamps is five more than the number of 13 cent stamps. the total value of all the stamps is $2.60. find the number of 13 cent stamps in collection.
TWICE THE 5 C STAMPS=2F
ONE LESS=2F-1=T......2F=T+1.....F=(T+1)/2=0.5(T+1).............I
5 MORE THAN 13 C STAMPS =T+5=E.........................II
VALUE OF 5 C STAMPS=5F
.........13........=13T
.........18........=18E
TOTAL VALUE=5F+13T+18E=260......................III
5*0.5(T+1)+13T+18(T+5)=260
2.5T+2.5+13T+18T+90=260
33.5T=260-90-2.5=167.5
T=167.5/33.5=5
NUMBER OF 13 C STAMPS =5