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Word Problem

In a certian year, brand A of heart rate watch cost $37.55 and brand B cost $56.55. A non profit community health organization purchased 32 heart rate watches for use at a wellness center. If the organization spent 1410.60 for the watches how many of each type did they purchase?
 
The Organization purchased ____ heart rate watches of brand A and ___Heart rate watches of brand B
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1 Answer

Hey Shawn,
 
For this word problem, we can set up two equations, since we have two unknowns (A and B). These equations can be set up as follows, where A and B represent the # of heart rate watches for each brand:
 
1. A + B = 32
 
2. 37.55A + 56.55B = 1410.60
 
I prefer the "elimination" method for solving this system of equations. Let's perform the calculations and solve! So we can multiply the first equation by -37.55 to eliminate the A term:
 
1. -37.55 [ A + B = 32] => -37.55A - 37.55B = -1201.6
 
Then we can add the two equations together:
 
1. -37.55A - 37.55B = -1201.6
2. 37.55A + 56.55B = 1410.60
 
The result:
 
19B = 209
 
B=11
 
If we know B, we can go back into either of the two original equations. Lets do the first equation since its easier to solve for A:
 
A + B = 32
 
A + (11) = 32
 
A = 21
 
Hope this break down helps you to understand word problems a little bit better! :)
 
Alex