Answer:
Brand A = 21 heart-rate watches.
Brand B = 13 heart-rate watches.
Step-by-step explanation:
Let A be the number of Brand A heart watches and B be the number of Brand B heart watches.
We have been given that a nonprofit community health organization purchased 34 heart-rate watches for use at a wellness center.
We can represent this information in an equation as:
![A+B=34...(1)](https://tex.z-dn.net/?f=A%2BB%3D34...%281%29)
We have been given that in a certain year, brand A of heart-rate watch cost $39.99 and brand B cost $59.99 and the organization spent $1619.66 for the watches.
We can represent this information in an equation as:
![39.99*A+59.99*B=1619.66...(2)](https://tex.z-dn.net/?f=39.99%2AA%2B59.99%2AB%3D1619.66...%282%29)
We will use substitution method to solve our system of equations.
From equation (1) we will get,
![A=34-B](https://tex.z-dn.net/?f=A%3D34-B)
Substituting
in equation(2) we will get,
![39.99*(34-B)+59.99*B=1619.66](https://tex.z-dn.net/?f=39.99%2A%2834-B%29%2B59.99%2AB%3D1619.66)
![-39.99*B+59.99*B=1619.66-1359.66](https://tex.z-dn.net/?f=-39.99%2AB%2B59.99%2AB%3D1619.66-1359.66)
![20*B=260](https://tex.z-dn.net/?f=20%2AB%3D260)
![B=\frac{260}{20}](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B260%7D%7B20%7D)
Therefore, the organisation purchased 13 heart-rate watches of brand B.
Now let us substitute B=13 in equation (1).
![A+13=34](https://tex.z-dn.net/?f=A%2B13%3D34)
![A+13-13=34-13](https://tex.z-dn.net/?f=A%2B13-13%3D34-13)
![A=21](https://tex.z-dn.net/?f=A%3D21)
Therefore, the organisation purchased 21 heart-rate watches of brand A.