Question

Suppose that $17$ inches of wire costs $51$ cents. At the same rate, how many inches of wire can be bought for $42$ cents?

Answer 1

Hint: In the above question, we have been given that $17$ inches of wire cost $51$ cents. This means that for $51$ cents, we can buy a total of $17$ inches of wire. For determining the number of inches of wire, which can be bought for the given amount, we need to use the unitary method so as to find out the number of inches of wire which can be obtained from one cent. This can be done by dividing $17$ inches by $51$ so that we will obtain $\dfrac{1}{3}$ inches. Finally, on multiplying this measurement by $42$ cents, we will obtain the required number of inches of wire which can be bought for $42$ cents.

Complete step by step solution:
According to the question, $51$ cents are equivalent to $17$ inches of wire.
Therefore, by unitary method, $1$ cent must be equivalent to $\dfrac{17}{51}=\dfrac{1}{3}$ inches of wire.
This implies that the $42$ cents must be equivalent to $\dfrac{1}{3}\times 42=14$ inches of wire.

Hence, $14$ inches of wire can be bought for $42$ cents.

Note: We must be careful of what is to be found out in terms of what while solving these types of questions. For example, in this question, we were asked to find out the inches of wire which can be bought for a given number of cents. Therefore, we obtained the inches of wire equivalent to one cent. Do not obtain the cost of one inch, which might sound more sensible, while solving this question.