Question

joe has a ring weighing 14 grams made of an alloy of 14 % silver and the rest gold. he decides to melt down the rings and add enough silver to reduce the gold content to 68 % . how many grams of silver should he add?

Answer 1

With the help of the ratio method, we conclude that 72 grams of sugar should be added.

What is Ratio Method?

• In the ratio method, we compare two quantities by equating their two ratios; this equation is also referred to as a proportion.
• The cross-multiplication method will be used to solve it.

So, 'n=5' will be the number of rings.

• 'w = 18 grams' will be the weight of each ring.
• Total weight: w₀ = n × w = 5 × 18 = 90 grams

Let 's' be silver. Then,

• New weight: wₙ = s + 90
• Old % of gold: p₀ = 90% = 0.9
• New % of gold: pₙ = 50% = 0.5

Now, use the ratio method as follows:

• $\frac{w_o}{w_n}=\frac{p_n}{p_o}$
• $\frac{90}{s+90}=\frac{0.5}{0.9}$
• 90 × 0.9 = 0.5 × (s + 90)
• 81 = 0.5s + 0.5 × 90
• 81 = 0.5s + 45
• 81 - 45 = 0.5s
• 36 = 0.5s
• 36/0.5 = s
• 72 = s
• So, s = 72
  

Therefore, with the help of the ratio method, we conclude that 72 grams of sugar should be added.

Know more about Ratio Method here:

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The correct question is given below:
A jeweler has five rings, each weighing 18 grams, made of alloys of 10% silver and 90% gold. He decides to melt down the rings and add enough silver to reduce the gold content to 50%. How much silver should he add?