i have to solve system of equations

Question

Ms. Martinez had a jewelry party for all of her friends. She sold 32 pieces of Jealert for a total of $1050. The brackets sold for $39?each, and the necklaces sold for $35 each. How many bracelets did Ms. Martinez sell to her friends. How many necklaces did shape sell.

Answer 1

Okay, Leah,

 

Let's use B and N as the quantities for which we are looking.

 

The total number of items sold = B + N = 32.

 

The total cost of items sold is the number sold multiplied by the cost per item added together = B*39 +N*35 = 1050.

 

Solve the first equation for either variable so that you can substitute that variable into the second equation:

 

B = 32 - N

 

39B + 35N = 39(32 - N) + 35N = 1050

 

Multiply through the parentheses and combine the terms with N:

 

39*32 - 39*N + 35*N = 1248 - 4N = 1050

 

Add 4N to both sides and subtract 1050 from both sides:

 

1248 - 4N + 4N - 1050 = 1050 + 4N - 1050

 

1248 - 1050 = 4N

 

198 = 4N

 

198/4 = 4N/4

 

49.5 = N

 

B = 32 - N = 32 - 49.5 = -17.5

 

This does not make sense realistically but it does after checking all my work it does mathematically, so be sure to check by substituting the values into the total cost equation:

 

39B + 35N = 1050

 

39*(-17.5) + 35*(49.5) = 1050.

 

So, one of the four numbers quoted in the original statement must have been misquoted. A larger total than $1050 (< $1248) would give a smaller N and could give a positive B.

 

Check you work. You can use the same steps with the new numbers to get your answer.

 

Michael.