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

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:

$A+B=34...(1)$

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,

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

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

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

$20*B=260$

$B=\frac{260}{20}$

$B=13$

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.