Question

a hotel purchased 51 bath towels and 78 washcloths for a total cost of $1335. a second purchase of 61 bath towels and 41 washcloths at the same prices, cost $1283. find the individual prices of the bath towels and washcloths.

Answer 1

bath towels: $17

washcloths: $6

Explanation:

If we let t and w represent the costs of towels and washcloths respectively, the problem statement tells us the combinations of costs are ...

51t +78w = 1335

61t +41w = 1283

These equations are readily solved by any of several techniques. One of my favorite is to let a calculator do it. Most graphing calculators are capable of solving equations like these represented as an augmented matrix:

`\left[\begin{array}c51&78&1335\\61&41&1283\end{array}\right]`

An appropriate function for the purpose is one that reduces the matrix to row-echelon form. Then the right-most column is the values of the variables that satisfy the equations.

Here, we get t=17, w=6.

The price of a bath towel is $17; the price of a washcloth is $6.