Question

Hi! i think this question is super hard and i cant understand it. it goes like this

A goldsmith has a bracelet that weighs 20 grams. Of the weight of the bracelet 60% is gold and 40% silver.

a) How many grams of silver does the bracelet contain?

The goldsmith will now make a new bracelet with a halved portion of silver, ie a bracelet where the proportion of silver is half as large. The goldsmith will now make a new bracelet with a halved portion of silver, ie a bracelet where the proportion of silver is half as large. This makes the goldsmith by melting down the original bracelet and adding more gold so that the proportion of silver becomes 20%. The weight of silver will thus be as great in the new bracelet as in the original bracelet, but the total weight will increase.

b) How many grams of gold does the goldsmith need to halve the proportion of silver in the new bracelet so that it consists of 20% silver?

c) The goldsmith should do the same for two other bracelets which from the beginning weigh 30 grams and 40 grams respectively. in both bracelets, the proportion of silver is 40%. How many grams of gold do the goldsmith have to add in each bracelet for the proportion of silver to be halved?

d) What conclusion can you draw about the added weight of gold in relation to the weight of the bracelet?

e) Show that your conclusion applies regardless of the weight of the bracelets.

f) The goldsmith wants to halve the silver content in bracelets, which from the beginning consists of other proportions of gold and silver than 60% and 40%. Check if your conclusion also applies to these bracelets.

Answer 1

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