Algebra word problem?

Question

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.

Answer 1

x = # of 5c stamps
y = # of 13c stamps
z = # of 18c stamps

you'll come up with three equations from the information in the problem:

Total value of all stamps is $2.60, thus
0.05x + 0.13y + 0.18z = 2.60

The number of 13 cent stamps is 1 less than twice the number of 5 cent stamps, Thus
y = 2x - 1

Number of 18 cent stamps is 5 more than the number of 13 cent stamps, thus
y + 5 = z

Substituting in for y
z = 2x - 1 + 5

Substituting y & z in the first equation (so you only have x variables)
0.05x + 0.13(2x-1) + 0.18(2x - 1 + 5)
0.05x + .26x - .13 + .36x + 72 = 2.60
0.67x + .59 = 2.60
x = 3

thus y = 5

Answer 2

5

Answer 3

I'll provide translation tip:

Let
A = the number of 5-cent stamps
B = the number of 13-cent stamps
C = the number of 18-cent stamps

The number of 13 cent stamps is one less than twice the number of 5 cent stamps.
(The number of 13 cent stamps) is (one less than) twice (the number of 5 cent stamps)
(B) is (1 less than) twice (A)
(B) is (1 less than) (twice A)
(B) is (1 less than (2*A)
(B) = (1 less than 2A)
B = 2A -1

The number of 18 cent stamps is five more than the number of 13 cent stamps.
(The number of 18 cent stamps) is five more than (the number of 13 cent stamps.)
(C) is five more than (B)
C is (5 more than B)
C is (5 + B)
C = (5 + B)
C = 5 + B

The total value of all the stamps is $2.60 means

value of 5-cent stamps + value of (13-cent stamps) + value of(18-cent stamps) = 2.60
(number of 5-cent stamps * .05) + (number of 13-cent stamps * 0.13) + (number of 18-cent stamps * 0.18) = 2.60
(A * 0.5) + (B * 0.13) + (C * 0.18) = 2.60
0.5A + 0.13B + 0.18C = 2.60

now, you have three equations:
B = 2A -1
C = 5 + B
0.5A + 0.13B + 0.18C = 2.60

and solve for A, B, C.

Answer 4

Let's call this f, t, and e.

2f - 1 = t
e = t + 5 = (2f - 1) + 5 = 2f + 4

5f + 13t + 18e = 260

5f + 13(2f - 1) + 18(2f + 4) = 260

5f + 26f - 13 + 36f + 72 = 260

67f + 59 = 260

67f = 201

f = 3

2f - 1 = t
2 * 3 - 1 = 5
t = 5