Word Problem Algebra

Question

Timothy's new stamp collection includes 18,22,26 and 14 cent stamps. The collection has two thirds as many 22 cent stamps as 18 cent stamps, one fewer 26 cent stamps than 22 cent stamps, and three more than twice as many 14 cent stamps as 22 cent stamps. How many of each type of stamp is in his collection if it's total value is $6.34

Answer 1

Let x = the number of 18 cent stamps

Let (2/3)x = the number of 22 cent stamps

Let (2/3)x - 1 = the number of 26 cent stamps

Let 2(2/3)x + 3 = the number of 14 cent stamps

 

.18x + .22(2/3)x + .26[(2/3)x - 1] + .14[2(2/3)x + 3] = 6.34    Multiply both sides of the equation by 100.

18x + (44/3)x + (52/3)x - 26 + (56/3)x + 42 = 634

18x + (14 2/3)x +  (17 1/3)x - 26 + (18 2/3)x + 42 = 634

(68 2/3)x = 618

(206/3)x = 618     Multiply both sides by 3/206

x = 9   18 cent stamps

(2/3)(9) = 6   22 cent stamps

6 - 1 = 5     26 cent stamps

2(6) + 3 = 15      14 cent stamps

 

That was some problem!!!

   

 

 

 

 

 

 

    

ply both sides of the eq