Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Vera is selling her handmade jewelry online. Yesterday, she sold 5 bracelets and 6 necklaces, for a profit of $181. Today, she made a profit of $191 by selling 7 bracelets and 6 necklaces. How much profit does Vera earn from each piece? Vera earns a profit of $____ from every bracelet and $___from every necklace.

Please help me out with this!

Answer 1

bracelet = $5, necklace = $26

Explanation:

so first we need to form the equations.

(note that x = bracelets, y = necklaces)

1st equation: 5x + 6y = 181

2nd equation: 7x + 6y = 191

-you want to try to make one of the variables equal on both equations, just like 6y on the 1st and 2nd equation

1) since both 6y's from both equations are positive, you want to subtract them so y does not exist anymore.

2) subtract 7x from 5x

3) subtract 191 from 181

4) your answer should be -2x = -10, which equals x = 5 when you simplify it

-so now we know that each bracelet costs $5

-to find the cost of each necklace:

1) plug in the value of x into either 1st or 2nd equation.

2) for example:

5x + 6y = 181 -first equation

5(5) + 6y = 181 -plug in

25 + 6y = 181 -distribute

6y = 156 - leave 6y alone by subtracting 25 from both sides

y = 26 -divide by 6 to get the value of y

-so now we know that each necklace costs $26

(you can either solve it by substitution or elimination, but since elimination is easier in this problem I used it rather than substituting)