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Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

The owner of two hotels is ordering towels. He bought 89 hand towels and 5 bath towels for his hotel in Westford, spending a total of $213. He also ordered 35 hand towels and 53 bath towels for his hotel in Lowell, spending $441. How much does each towel cost?

A hand towel costs $__________ and a bath towel costs $_________

Answer 1

Hi Antonia. This one only sounds scary when you read it.

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

The owner of two hotels is ordering towels. He bought 89 hand towels and 5 bath towels for his hotel in Westford, spending a total of $213. He also ordered 35 hand towels and 53 bath towels for his hotel in Lowell, spending $441. How much does each towel cost?

A hand towel costs $__________ and a bath towel costs $_________

Always start with what you know. Let's use H for hand towels and B for bath towels.

89 hand towels plus 5 bath towels costs $213, which gives us this equation:

89H+5B=213

35 hand towels plus 53 bath towels costs $441, gives us this equation:

35H+53B=441

Looking at them together:

89H+5B=213

35H+53B=441

solve the easiest equation for B. I chose the first one:

89H+5B=213

5B=213-89H

B=(213-89H)/5

You can stop there for now, no real need to go further finding B. This is the first step in ELIMINATION. Next we replace our B with (213-89H)/5 in the second equation and solve for H:

35H+53((213-89H)/5)=441

35H +53(42.6-17.8H)=441

35H+2257.8-943.4H=441

35H-943.4H=-1816.8

-908.4H=-1816.8

H=$2

Almost there. Now we go back to the first equation and replace H with 2 and solve for B. I used the B=(213-89H)/5 form:

B=(213-89*2)/5

B=(213-178)/5

B=35/5

B=$7

So, hand towels cost $2 and bath towels cost $7. Always check your work by recalculating the equations with your new answers:

89*2+5*7=213

178+35=213✔

35*2+53*7=441

70+371=441✔