A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 5 grams and the amount of gold in each necklace is 22 grams. The jeweler made a total of 17 bracelets and necklaces using 238 grams of gold. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define the variables that you use to write the system.

Question

Mathematics

Luciano Powers

30 October, 02:18

A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 5 grams and the amount of gold in each necklace is 22 grams. The jeweler made a total of 17 bracelets and necklaces using 238 grams of gold. Write a system of equations that could be used to determine the number of bracelets made and the number of necklaces made. Define the variables that you use to write the system.

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Andreas Orr · Answer 1

The jeweler made 9 necklaces.

The jeweler made 8 bracelets.

Step-by-step explanation:

x = number of bracelets

y = number of necklaces

17 = x + y

238 = 5x + 22y

Make one of the coefficients, x, the same.

17 = x + y

Multiply this equation by 5.

85 = 5x + 5y

Subtract the equations to get rid of x.

(238 = 5x + 22y) - (85 = 5x + 5y)

(5x - 5x) + (22y - 5y) = 238 - 85

22y - 5y = 238 - 85

17y = 153

y = 153/17 = 9

The jeweler made 9 necklaces. Substitute this back into one of the equations to find x.

17 = x + y

17 = x + 9

17 - 9 = x

x = 8

238 = 5x + 22y

238 = 5x + 22 (9)

238 = 5x + 198

238 - 198 = 5x

40 = 5x

x = 40/5

x = 8

The jeweler made 8 bracelets.