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A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amount of gold in each necklace is 18 grams. The jeweler used 168 grams of gold and made 4 more necklaces than bracelets. Determine the number of bracelets made and the number of necklaces made.

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Answer:

There are 4 bracelets, and 8 necklaces made.

Step-by-step explanation:

Let:

  • bracelets be denoted by the variable, "x"
  • necklaces be denoted by the variable, "y"

Note: There are 4 more necklaces than bracelets.

The amount of gold in bracelets is 6 grams and the amount of gold in necklaces is 18 grams, and there are 168 grams of gold in all.

Set the system equations:

y = x + 4

168 = 6x + 18y

First, plug in x + 4 for y in the second equation:

168 = 6x + 18y

168 = 6x + 18(x + 4)

First, distribute 18 to all terms within the parenthesis:

168 = 6x + (18 * x) + (18 * 4)

168 = 6x + 18x + 72

168 = 24x + 72

Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Additions

Subtraction

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First, subtract 72 from both sides of the equation:

168 = 24x + 72

168 (-72) = 24x + 72 (-72)

168 - 72 = 24x

24x = 96

Next, divide 24 from both sides of the equation:

(24x)/24 = (96)/24

x = 96/24 = 4

x = 4.

Plug in 4 for x in one of the given equations:

y = x + 4

y = (4) + 4

y = 8

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There are 4 bracelets, and 8 necklaces made.

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