Vondra wants to buy a charm bracelet. Oak Grove Fine Jewelry charges $16 per charm, plus $53 for the bracelet. Sandoval Jewelers, in contrast, charges $27 per charm and $31 for the bracelet. If Vondra wants to add a certain number of charms to her bracelet, the cost will be the same at either jewelry shop. What would the total cost of the bracelet be? How many charms would that be?

The bracelet will cost 85$ and it'll have 2 charms.

Step-by-step explanation:

In order to find the total cost of the bracelet and how many charms it'd be we need to build an equation for each store. So we have:

Oak Grove:

total cost = 16*charm + 53

Sandoval:

total cost = 27*charm + 31

We then find the number of charm that'll make them equal, since the price has to be the same on both shops:

16*charm + 53 = 27*charm + 31

27*charm - 16*charm = 53 - 31

11*charm = 22

charm = 2

The cost of the bracellet is:

total cost = 27*2 + 31 = 85 $

The total cost of bracelet + the charms will be $85 at either shops.

The number of charms that will ensure the price becomes the same at either shops is 2

Step-by-step explanation:

Before proceeding to calculate, let us use "x" to represent that unknown number of charms that Vondra could purchase alongside a bracelet before the total cost of the items at either jewelry shops becomes equal.

So, if oak grove jewelry shop sells one charm for $16, then the total cost of that unknown number of charms that Vondra will have to purchase alongside a bracelet before it equals the cost in Sandoval store =

$16 * x = $16x (Total cost of the unknown number of charms at oak grove)

Adding this to the cost of a bracelet at oak grove:

53 + 16x (Total cost of bracelet and the unknown number of charms)

Now, that unknown number of charms that can be purchased at either shops for the cost of the items to become equal at both shops is "x"; so if a charm sells for $27 at Sandoval shop, then the total cost of the unknown quantity of charms at this shop is then:-

$27 * x = $27x (cost of the unknown number of items at Sandoval jewelers)

The cost of the bracelet and that unknown number of items at this shop = $31 + $27x

Recall that at the purchase of "x" number of charms, cost of the items (bracelet + charms) becomes equal at either shops. This means that:

53 + 16x = 31 + 27x

27x - 16x = 53 - 31

11x = 22

x = 22/11

x = 2 charms

Therefore, if Vondra decides to purchase a bracelet and 2 charms, the cost of the items become equal at either shops.

Since the total cost of the bracelet + the charms at oak grove = 53 + 16x, if we substitute x for 2, the total cost of the items at oak grove will now be:-

53 + 16 (2)

= 53 + 32

= $85

Again, the total cost of the items at Sandoval = 31 + 27x, we now substitute x for 2:

31 + 27 (2)

= 31 + 54

= $85

So we can see that purchasing two charms + bracelet will now make the cost of the items to become equal at either shops.