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.
