Question

If pencils sell at $6$ for $59$ cents, how many pencils can be bought for $\$2.95$?

Answer 1

Hint: The number of pencils has been asked for the given cost in dollars. But we are given the number of pencils sold at the amount in cents. So we need to convert the given cost in dollars to cents. For this, we need to use the conversion between dollar and cents which is given by $\$1=100\text{cents}$. Therefore, we will get $\$2.95=295\text{cents}$, for which we have to find out the number of pencils. We need to use the unitary method for solving this question. Since the number of pencils which can be bought for the given amount has been asked in the above question, we need to find the number of pencils which can be bought for one cent. Then multiplying that amount with $295$ cents, we will get the required number of pencils.

Complete step by step solution:
According to the question, $6$ pencils are sold for $59$ cents.
Using the unitary method we can say that $\dfrac{6}{59}$ pencils can be sold for $1$ cent.
Now, we have been asked to find out the number of pencils for $\$2.95$ dollars. We know that $\$1=100\text{cents}$. Therefore, we will get $\$2.95=295\text{cents}$. So effectively, we have to find out the number of pencils for $295$ cents. Since one cent is equivalent to $\dfrac{6}{59}$ pencils, $295$ cents will be equivalent to $\dfrac{6}{59}\times 295=30$ pencils.

Hence, $30$ pencils can be bought for $\$2.95$.

Note: For solving this question, we need to be familiar with the conversion between the dollars and the cents. We can appreciate that this conversion is similar to the familiar conversion between the rupees and paise, which is given by $1\text{ rupee}=100\text{ paisa}$. Also, do not get confused by the $\dfrac{6}{59}$ pencil, which we got for one cent. While using the unitary method, such absurd results are common.