Question

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.

Answer 1

Number of bracelets made is 4 and number of necklace made is 8

Solution:

Let "b" be the number of bracelets made

Let "n" be the number of necklace made

amount of gold in 1 bracelet = 6 grams

amount of gold in 1 necklace = 18 grams

Given that he made 4 more necklaces than bracelets

number of necklace made = 4 + number of bracelets made

n = 4 + b -------- eqn 1

The jeweler used 168 grams of gold

Therefore, we can frame a equation as:

number of bracelets made x amount of gold in 1 bracelet + number of necklace made x amount of gold in 1 necklace = 168

$b \times 6 + n \times 18 = 168$

6b + 18n = 168 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

6b + 18(4 + b) = 168

6b + 72 + 18b = 168

24b = 168 - 72

24b = 96

b = 4

From eqn 1,

n = 4 + b

n = 4 + 4

n = 8

Thus number of bracelets made is 4 and number of necklace made is 8