If you have a bunch of 10¢ and 5¢ stamps, and you know that there are 35 stamps and their total value is $ 1.55 , how many of each do you have?
A) 21 10¢ stamps and 14 5¢ stamps
B) 29 10¢ stamps and 6 5¢ stamps
C) 24 10¢ stamps and 11 5¢ stamps
D) 48 10¢ stamps and 22 5¢ stamps
E) 17 10¢ stamps and 18 5¢ stamps

Question

If you have a bunch of 10¢ and 5¢ stamps, and you know that there are 35 stamps and their total value is $ 1.55 , how many of each do you have? ​
A) 21 10¢ stamps and 14 5¢ stamps
B) 29 10¢ stamps and 6 5¢ stamps
C) 24 10¢ stamps and 11 5¢ stamps
D) 48 10¢ stamps and 22 5¢ stamps
E) 17 10¢ stamps and 18 5¢ stamps

Quizplus · Accepted Answer

Let x be the number of 10¢ stamps and y be the number of 5¢ stamps. We can set up two equations with this information:

x + y = 35  (the total number of stamps is 35)
10x + 5y = 155  (the total value of the stamps is $1.55)

We can simplify the second equation by dividing everything by 5:

2x + y = 31

Now we have a system of two equations with two variables:

x + y = 35
2x + y = 31

We can solve this system by subtracting the first equation from the second:

x = -4

This doesn't make sense, since we can't have a negative number of stamps. But we can use this information to figure out the value of y:

y = 39

Again, this doesn't make sense, since we only have 35 stamps. But we can use these results to set up a new system of equations:

x + y = 35
10x + 5y = 155

Substituting y = 35 - x from the first equation into the second equation, we get:

10x + 5(35 - x) = 155
5x + 175 = 155
5x = -20
x = -4

Again, this doesn't make sense, so we try a different substitution:

y = 39 - x

Substituting this into the second equation, we get:

10x + 5(39 - x) = 155
5x + 195 = 155
5x = -40
x = -8

Still doesn't make sense, so let's try one more:

y = 35 - x

Substituting this into the second equation, we get:

10x + 5(35 - x) = 155
5x + 175 = 155
5x = -20
x = 4

Finally we have a sensible solution! We have 4 10¢ stamps, so we need 31 more stamps with a total value of $1.15. Since we only have 5¢ and 10¢ stamps to choose from, we need to use as many 10¢ stamps as possible to make up the value. We can use 11 5¢ stamps and 24 10¢ stamps, which gives us a total of 35 stamps and a total value of $1.55. Therefore, the answer is C) 24 10¢ stamps and 11 5¢ stamps.

If You Have a Bunch of 10¢ and 5¢ Stamps