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,

$\frac{(6y)}{6} =\frac{240}{6}$

$y =\frac{240}{6}$

$y = 40$

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.