Question

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. He also ordered 45 hand towels and 71 bath towels for his hotel in Middletown, spending $587. How much does each towel cost?

Answer 1

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

$x = \frac{2606}{1303}$

x =$ 2

Putting this x = 2 in the equations

1395 × 2  + 2201y = 18197

2790 + 2201y = 18197

2201y = 15407

$y = \frac{15407}{2201}$

y = $7

Therefore the cost of the hand towels is $2 and cost of the bath towels is $7 .