Question

Suppose that 19 inches of wire costs 76 cents. At the same rate, how many inches of wire can be bought for 52 cents?

Answer 1

Hint: In the given question, we have been asked to find out the inches of wire that can be bought in 52 cents and it is given that 19 inches of wire costs 76 cents. In order to find out, we need to use the unitary method for solving that means here we have to find the cost of 1 inch of wire first. We find the cost of 1 inch of wire by dividing the cost of 9 inch of wire to the total quantity bought. Then after getting the cost of 1 inch of wire, we will divide the total cents given i.e. 52 by the cost of 1 inch of wire. In this way we will get our required solution.

Complete step-by-step solution:
We have given that,
19 inches of wire cost 76 cents.
Thus,
Cost of 19 inches of wire = 76 cents
Cost of 1 inch of wire = \[\dfrac{\cos t\ of\ 19\ inches\ of\ wire}{total\ quantity\ of\ inch\ given}=\dfrac{76}{19}=4\]
Thus, cost of 1 inch of wire = 4 cents
Now,
Inches of wire that can be bought in 52 cents = \[\dfrac{total\ cents\ given}{\cos t\ of\ 1\ inch\ of\ wire}=\dfrac{52}{4}=13\]

Therefore, 13 inches of wire can be bought in 52 cents.

Note: In order to solve these types of questions, we have to use the unitary method for solving. Unitary method is used to find the value of a unit i.e. value of a 1 thing from the value of a multiple. Here we find cost of 1 inch of wire by using the cost of 19 inches of wire. In the unitary method, we get the amount for 1 unit always.