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?

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eurydike eurydike · Answer 1 · 2018-09-06T08:25:10+02:00

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, [tex] x+y = 120[/tex]....equation 1

Now given the price of bracelet = $7

So, the price of x bracelets = $ [tex] (7)(x)[/tex] =$ [tex] (7x) [/tex]

Given, the price of necklace = $13.

So, the price of y necklaces = $ [tex] (13)(y)[/tex] = $ [tex] (13y)[/tex]

The total amount for the jewellery given = $ 1080.

We can write the equation as,

[tex] 7x + 13y = 1080[/tex]....equation 2

Now from equation 1, we can write,

[tex] x = 120-y[/tex]

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

[tex] 7(120-y) + 13y = 1080[/tex]

[tex] 840-7y+13y = 1080 [/tex]

[tex] 840+6y = 1080 [/tex]

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

[tex] 840+6y-840 = 1080-840[/tex]

[tex] 6y = 1080-840[/tex]

[tex] 6y = 240[/tex]

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

[tex] \frac{(6y)}{6} =\frac{240}{6}[/tex]

[tex] y =\frac{240}{6}[/tex]

[tex] y = 40[/tex]

So we have got the number of necklaces = 40

Now we have, [tex] x = 120-40[/tex]

[tex] x = 80[/tex]

So, the number of bracelets = 80

We have got the required answer here.