James had enough money to buy either 48 pens or 60 pencils. If he had already bought 8 pens and 16 pencils, how many more pencils can James buy?
James originally had enough money to buy either 48 pens or 60 pencils, so he must have had enough money to buy 1 pen for the same price as 5/6 of a pencil (since 60 ÷ 48 = 5/4).
If James already bought 8 pens and 16 pencils, that's equivalent to buying the cost of 8 pens + 16 pencils = 8*(5/6) pencils + 16 pencils = 40/6 pencils + 96/6 pencils = 136/6 pencils.
Therefore, James has 136/6 pencils worth of money left. To find out how many more pencils he can buy, we divide this amount by the price of 1 pencil:
(136/6) ÷ (5/6) = (136/6) x (6/5) = 136/5
So James can buy another 136/5 pencils, which is equivalent to 27 and 1/5 pencils.
To find out how many more pencils James can buy, we need to calculate the remaining money he has after buying 8 pens and 16 pencils.
Let's first find out how much money James has:
If James can buy 48 pens with all his money, then the cost of one pen would be the total amount of money divided by 48.
Let's represent the cost of one pen as 'P'.
P = Total amount of money ÷ Number of pens
P = Total amount of money ÷ 48
Similarly, if James can buy 60 pencils with all his money, then the cost of one pencil would be the total amount of money divided by 60.
Let's represent the cost of one pencil as 'N'.
N = Total amount of money ÷ Number of pencils
N = Total amount of money ÷ 60
Since we know that James bought 8 pens and 16 pencils, we can calculate the money spent on them.
Total money spent on pens = Cost of one pen × Number of pens bought
Total money spent on pens = P × 8
Total money spent on pencils = Cost of one pencil × Number of pencils bought
Total money spent on pencils = N × 16
Now, we can subtract the total money spent on pens and pencils from the total amount of money James had to find the remaining money.
Remaining money = Total amount of money - Total money spent on pens - Total money spent on pencils
Finally, we can use the remaining money to calculate how many more pencils James can buy:
Number of pencils James can buy = Remaining money ÷ Cost of one pencil
With these calculations, we can find out how many more pencils James can buy.