How much was each item

Question

Christopher Columbus spent 20 pieces of silver at the Mainer's Hall.  He bought a hat, a cape, and a spyglass.  the spyglass cost 9 more pieces of silver than the cape.  The spyglass and the cape together  cost 16 more pieces of silver than the hat.  How much did he pay for each item?

Answer 1

So we know the total spent was 20

 

Let h = cost of the hat

c = cost of the cape

s = cost of the spyglass

 

The spyglass cost 9 more than the cape, so s = c+9

The spyglass and cape together cost 16 more than the hat, so s+c = h + 16

 

The total is s+c+h = 20

 

Now we can substitute what we found from above:

Since s+c = h+16 our equation for the total becomes (h+16)+h = 20, or 2h+16 = 20, which becomes 2h= 4, so h = 2

 

Now we can say s+c = h+16, or s+c = 2+16, which is s+c = 18

 

We can rewrite this as s = 18-c

 

From the first equation we also know s=c+9

Therefore, 18-c = c+9, which becomes 9 = 2c, so c = 4.5

 

Since s = 18-c, s = 18-4.5 or s = 13.5