Question

10

Answer 1

This question was not written properly

Complete Question

Steve has 54 stamps in his collection of 13 cent, 29 cent, and 45 cent stamps, totaling a value of $15.98. If the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80. Find the number of each type of stamp in his collection.

Answer:

a) The number of 13 cent = 14

b) The number of 29 cent = 24

c) The number of 45 cent = 16

Step-by-step explanation:

We are told he has 54 stamps in total.

These stamps are;13 cent, 29 cent, and 45 cent stamps.

Let's

Number of 13 cent = a

Number of 29 cent = b

Number of 45 cent = c

Hence,

a + b + c = 54........... Equation 1

The total value of the 3 stamps are $15.98.

1 cent = $0.01

We have

0.13a + 0.29b + 0.45c= $15.98 ......... Equation 2

We know from the question that:

13 cent stamps is doubled, the new total value of his stamp collection would be $17.80.

Therefore

2(0.13a) + 0.29b + 0.45c = 17.8

0.26a + 0.29b + 0.45c = 17.8 ......... Equation 3

Combining Equation 2 and 3 together

0.13a + 0.29b + 0.45c= 15.98 ......... Equation 2

0.26a + 0.29b + 0.45c = 17.8 ......... Equation 3

We eliminate b and c by Subtracting Equation 3 from 3

0.13a = 1.82

a = 1.82/0.13

a = 14

a + b + c = 54........... Equation 1

Since a = 14

14 + b + c = 54

b + c = 54 - 14

b + c = 40

c = 40 - b

Substitute 40 - b for c and 14 for a is Equation 2

0.13a + 0.29b + 0.45c= 15.98 ......... Equation 2

0.13(14 ) + 0.29b + 0.45(40 - b) = 15.98

= 1.82 + 0.29b + 18 - 0.45b = 15.98

Collect like terms

1.82 + 18 - 15.98 = 0.45b - 0.29b

3.84 = 0.16b

b = 3.84/0.16

b = 24

Hence: Solving for c

a + b + c = 54........... Equation 1

14 + 24 + c = 54

38 + c = 54

c = 54 - 38

c = 16

Therefore,

The number of 13 cent = 14

The number of 29 cent = 24

The number of 45 cent = 16