There are three methods we can use to solve this system
of equations. They are "Graphing, Substitution, and Elimination" methods. Let's apply the "Elimination" method...
Let....
h=cost of hand towel
b=cost of bath towel
Let's write a system of equations from the give information in
the problem statement...
59h+25b=570......Eq1, Bradford hotel
49h+32b=597......Eq2, Olean hotel
Our solution strategy: attempt to eliminate the "b" term by modifying both equations. We will...
multiply Eq1 by 32,
multiply Eq2 by (-25),
to get....
1888h+800b= 18240.....Eq1a
-1225h -800b=-14925.....Eq2a
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663h = 3315......."b" terms cancel
∴ h = 5............divide both sides by 663
Now substitute "h=5" into one of the original equations and solve
for "b". Let's use Eq1...
59(5)+25b=570......substitute "h=5"
295+25b=570.......simplify
25b=275......subtract 295, both sides
∴ b=11........divide both sides by 25
Substitute these values into both original
equations Eq1 and Eq2 to check for truth...
59(5)+25(11)=570
295+275=570
570=570.......true, √check
49(5)+32(11)=597
245+352=597
597=597.......true, √check
Always check your work and solutions.
The values for "h" and "b" are correct. So the
cost of the hand towel is $5.00 and the
cost of the bath towel is $11.00.
Now apply the other two methods to solve for "h" and "b".
