Question

In a certain​ year, brand A of​ heart-rate watch cost ​$39.99 and brand B cost ​$59.99. A nonprofit community health organization purchased 34 ​heart-rate watches for use at a wellness center. If the organization spent ​$1619.66 for the​ watches, how many of each type did they​ purchase?

Answer 1

Brand A = 21 heart-rate watches.

Brand B = 13 heart-rate watches.

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)`

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)`

We will use substitution method to solve our system of equations.

From equation (1) we will get,

`A=34-B`

Substituting
`A=34-B` in equation(2) we will get,

`39.99*(34-B)+59.99*B=1619.66`

`1359.66-39.99*B+59.99*B=1619.66`

`-39.99*B+59.99*B=1619.66-1359.66`

`20*B=260`

`B=(260)/(20)`

`B=13`

Therefore, the organisation purchased 13 heart-rate watches of brand B.

Now let us substitute B=13 in equation (1).

`A+13=34`

`A+13-13=34-13`

`A=21`

Therefore, the organisation purchased 21 heart-rate watches of brand A.