Check the picture below.
since chords NQ and MP cross the center of the circle at R, that means that those two chords are diametrical chords and the angles made by both are vertical angles and thus twin angles, namely both are 18° as you see in the picture, so the angle NMP in magenta is really 162° + 18° + 18° = 198°, and we know the radius NR is 8.
Answer:
Cost of the hand towels is $2 and cost of the bath towels is $7 .
Step-by-step explanation:
Let us assume that the cost of hand towels be x .
Let us assume that the cost of bath towels be y .
As given
The owner of two hotels is ordering towels.
He bought 38 hand towels and 31 bath towels for his hotel in Arcadia, spending a total of $293.
Than the equation becomes
38x + 31y = 293
As given
He also ordered 45 hand towels and 71 bath towels for his hotel in Middletown, spending $587.
Than the equation becomes
45x + 71y =587
Multiply the equation 45x + 71y =587 by 31 .
45x × 31 + 71y × 31 = 587 × 31
1395x + 2201y = 18197
Multiply 38x + 31y = 293 by 71.
71 × 38x + 71 × 31y = 293 × 71
2698x + 2201y = 20803
Thus two equations are
1395x + 2201y = 18197
2698x + 2201y = 20803
Subtracting 1395x + 2201y = 18197 form 2698x + 2201y = 20803 .
2698x - 1395x + 2201y - 2201y = 20803 - 18197
1303x = 2606
x =$ 2
Putting this x = 2 in the equations
1395 × 2 + 2201y = 18197
2790 + 2201y = 18197
2201y = 15407
y = $7
Therefore the cost of the hand towels is $2 and cost of the bath towels is $7 .