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 .