10 Steve has 54 stamps in his collection of 13€,

294, and 45¢ stamps, totaling a value of $15.98.

If the number of 13¢ 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.

A) 14- 13€, 24 - 294, 16 - 45€

they felt like it

B) 16- 134, 25 - 294, 13- 45°

she lost a bet

C) 15 - 13€, 24-29€, 15 - 45°

she was bored

D) 15 - 13€, 25 - 294, 14- 454

she thought it was cool

E) 14- 13¢, 25 - 29%, 15 - 45°

it would be fun

Gina Wison II Ting Alpebra LC), 2016

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.

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