Ahotel 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.

bath towels: $17

washcloths: $6

Step-by-step 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:

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.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.