Question in the description.

Question

Dee dees custom jewelry store sells hand made necklaces and bracelets. It costs the store $2.30 to buy supplies to make a necklace and $1.80 to buy supplies to make a bracelet. The store sells necklaces for $6.50 and bracelets for $4.70. Last christmas they spent $107.20 on materials for both products. They finished products for $289.80. How many necklaces and bracelets did they make last christmas?

Answer 1

Let N = number of necklaces 

Let B = number of bracelets

 

Spent $107.20  ==>  2.30*N + 1.80*B = 107.20

 

Finished products $289.80  ==>  6.50*N + 4.70*B = 289.80  

 

Solve the first equation for B 

 

1.80*B = 107.20 - 2.30*N

B = 10720/180 - (230/180)*N

B = 536/9 - (23/18)*N

 

Substitute this value for B into the second equation 

 

650*N + 470*(536/9 - (23/18)*N) = 28980

650*N + 251920/9 - (5405/9)*N = 28980

 

Multiply both sides by 9 to clear fractions 

 

5850*N + 251920 -5405*N = 260820

445*N = 8900

N = 20 

 

Plug this value into the original first equation and solve for B

 

2.30*(20) + 1.80*B = 107.20

46.00 + 1.80*B = 107.20

1.80*B = 61.20

B = 34 

 

They made 20 necklaces and 34 bracelets 

 

Check:  2.30*20 + 1.80*34 = 46 + 61.20 = $107.20 

            6.50*20 + 4.70*34 = 130 + 159.8 = $289.80