## Joanna bought only $0.15 stamps…

## Solution:

We are given that Joanna bought only $0.15 stamps and $0.29 stamps. We must determine how many $0.15 stamps Joanna bought.

**Statement One Alone: **

She bought $4.40 worth of stamps.

If we let x = the number of $0.15 stamps purchased and y = the number of $0.29 stamps purchased, we can create the following equation:

0.15x + 0.29y = 4.40

15x + 29y = 440

Although it appears that we do not have enough information to determine the value of x, we can actually manipulate the equation further to determine a value.

29y = 440 – 15x

29y = 5(88 – 3x)

y = 5(88 – 3x)/29

We must remember that x and y must be integers. Thus, 5(88 – 3x)/29 must be an integer. Since 29 does not divide into 5, 29 must divide into 88 – 3x. In other words, (88 – 3x) must be a multiple of 29. So we’re looking for an integer value of x that allows (88 – 3x) to be a multiple of 29.

Let’s list the multiples of 29 that are less than 88:

29 x 1 = 29

29 x 2 = 58

29 x 3 = 87

Thus, we know that (88 – 3x) must be a multiple of 29, that x must be an integer, and that the only possible multiples of 29 that are less than 88 are 29, 58, and 87. We need to determine which of these multiples of 29 will produce an integer value for x. We see immediately that (88 – 3x) cannot equal 87, so let’s check 29 and 58.

88 – 3x = 29

-3x = -59

x = 59/3, which is not an integer.

Let’s now check 58.

88 – 3x = 58

-3x = -30

x = 10

When x is 10, (88 – 3x) is a multiple of 29. Thus, the only possible value of x is 10. Since we know that Joanna bought ten $0.15 stamps, statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

**Statement Two Alone: **

She bought an equal number of $0.15 stamps and $0.29 stamps.

With the information in statement two we know that x = y. However, because we don’t have the total dollar amount of stamps she bought, this is not enough information to determine how many $0.15 stamps were sold. Statement two alone is not sufficient to answer the question.

**Answer: A**