Question

On a buying trip in los​ angeles, rosaria perez ordered 120 pieces of​ jewelry: a number of bracelets at ​$77 each and a number of necklaces at ​$1313 each. she wrote a check for ​$1 comma 0801,080 to pay for the order. how many bracelets and how many necklaces did rosaria​ purchase?

Answer 1

Let, the number of bracelets be x and the number of necklaces be y.

Given, there are 120 pieces of jewellery which are bracelets and necklaces.

So we can write the equation,
`x+y = 120`....equation 1

Now given the price of bracelet = $7

So, the price of x bracelets = $
`(7)(x)` =$
`(7x)`

Given, the price of necklace = $13.

So, the price of y necklaces = $
`(13)(y)` = $
`(13y)`

The total amount for the jewellery given = $ 1080.

We can write the equation as,

`7x + 13y = 1080`....equation 2

Now from equation 1, we can write,

`x = 120-y`

By substituting this value of x in equation 2, we will get,

`7(120-y) + 13y = 1080`

`840-7y+13y = 1080`

`840+6y = 1080`

Now we will move 840 to the right side by subtracting it from both sides. We will get,

`840+6y-840 = 1080-840`

`6y = 1080-840`

`6y = 240`

We can get y by moving 6 to the other side by dividing it to both sides. We will get,

`((6y))/(6) =(240)/(6)`

`y =(240)/(6)`

`y = 40`

So we have got the number of necklaces = 40

Now we have,
`x = 120-40`

`x = 80`

So, the number of bracelets = 80

We have got the required answer here.