Question

Seven bars of gold and nineteen bars of silver cost $1, 316,000. If silver cost 25%as much as gold, how much is one bar of gold and how much '12is one bar ofsilver?

Answer 1

We have to find the price of a bar of gold and the price of a bar of silver.

Lets call G the price of the bar of gold and S the price of the bar of silver.

We know that 7 bars of gold and 19 basr of silver cost $1,316,000.

We then can write this as an equation, knowing that the total cost is equal to the cost of the bars of gold plus the cost of the bars of silver, and each term is the number of bars times its price:

`7G+19S=1316000`

We also know that the silver costs 25% of the cost of gold, so we can write this as an equation too:

`S=0.25G`

We can use this second equation to replace S in the first equation and solve for G:

`\begin{gathered} 7G+19S=1316000 \\ 7G+19(0.25G)=1316000 \\ 7G+4.75G=1316000 \\ 11.75G=1316000 \\ G=(1316000)/(11.75) \\ G=112000 \end{gathered}`

With the value of G, we can now calculate the price of silver with the second equation:

`S=0.25\cdot G=0.25\cdot112000=28000`

Answer: the price of a bar of gold is $112,000 and the price of a bar of silver is $28,000.