In a certain year, brand A of a heart-rate watch cost $35.77 and brand B cost $56.77. A non-profit community health organization purchased 35 heart-rate watches for
use at a wellness center. If the organization spent $1504.95 for the watches, how many of each type did they purchase?
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To solve this problem, we can set up a system of equations to represent the given information.
Let's assume "x" represents the number of brand A heart-rate watches purchased, and "y" represents the number of brand B heart-rate watches purchased.
From the given information, we know the following:
1. The cost of brand A watches is $35.77 each. Therefore, the total cost of brand A watches is 35.77x.
2. The cost of brand B watches is $56.77 each. Therefore, the total cost of brand B watches is 56.77y.
3. The organization purchased a total of 35 watches. Therefore, the total number of watches is x + y.
Now, we can set up the equations using the given information:
Equation 1: 35.77x + 56.77y = 1504.95 (the total cost of the watches is $1504.95)
Equation 2: x + y = 35 (the total number of watches is 35)
To solve this system of equations, we can use substitution or elimination method. In this case, let's use the substitution method:
From Equation 2, we can rewrite it as x = 35 - y
Substitute x = 35 - y into Equation 1:
35.77(35 - y) + 56.77y = 1504.95
Simplify the equation:
1249.95 - 35.77y + 56.77y = 1504.95
Combine like terms:
20.00y = 255.00
Solve for y:
y = 12.75
Now substitute the value of y back into Equation 2 to find x:
x + 12.75 = 35
x = 22.25
Thus, the organization purchased 22 brand A heart-rate watches and 12 brand B heart-rate watches.