SOLUTION: A stamp collection consists 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 mor

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A stamp collection consists 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 mor      Log On


   

Question 116754: A stamp collection consists 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 the collection.
Here is what I have so far:
.05x + .13(2x+1) + .18((2x+1)-5)=2.60
Am I anywhere close? Can you help me solve?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let f be number of 5 cent stamps, t be numb. of 13 ct. stamps, e= numb 18 ct stamps.
t=2f-1
2f=t+1
f=(t+1)/2
.
e=t+5
.
.13t+.05f+.18e=2.60
.13t+.05((t+1)/2)+.18(t+5)=2.6
.13t+(.05t+.05)/2+.18t+.9=2.6
.13t+.025t+.025+.18t+.9=2.6
.335t+.925=2.6
.335t=2.6-.925
.335t=1.675
t=1.675/.335
t=5 13ct. stamps.
.
f=(5+1)/2=3 5ct. stamps.
.
e=5+5=10 18ct. stamps.
.
Always check:
5*.13+3*.05+10*.18
=.65+.15+1.80=$2.60
.
Ed