A woman buys 4 bags of
rice for ₦56 per bag and 3 bags of beans for ₦26 per bag using the currency “NAIRA” (₦) in base 7. What
is the total cost of the items in another currency
“ANTI” (₳) in base 8?
converting to base10
... rice ... 56b7 = (5 * 7) + (6 * 1) = 41b10 ... 4 bags are 164b10
... beans ... 26b7 = (2 * 7) + (6 * 1) = 20b10 ... 3 bags are 60b10
... total cost ... 224b10
converting to base 8 ... 111b8 = 64 + 8 + 1 = 73b10
... 224b10 = (3 * 64) + (4 * 8) = 340b8
To find the total cost of the items in the currency "ANTI" (₳) in base 8, we need to convert the prices of rice and beans from base 7 to base 8, and then calculate the total cost.
First, let's convert the price of rice from base 7 to base 10:
₦56 in base 7 = 5*7^1 + 6*7^0 = 5*7 + 6*1 = 35 + 6 = 41
So, the price of one bag of rice is ₦41 in base 10.
Next, let's convert the price of beans from base 7 to base 10:
₦26 in base 7 = 2*7^1 + 6*7^0 = 2*7 + 6*1 = 14 + 6 = 20
So, the price of one bag of beans is ₦20 in base 10.
Now, let's calculate the total cost of the items:
Total cost of rice = 4 bags * ₦41 = ₦164 in base 10
Total cost of beans = 3 bags * ₦20 = ₦60 in base 10
Finally, let's convert the total cost from base 10 to base 8:
₦164 in base 10 = (2*8^2) + (1*8^1) + (4*8^0) = 2*64 + 1*8 + 4*1 = 128 + 8 + 4 = 140
₦60 in base 10 = (7*8^1) + (4*8^0) = 7*8 + 4*1 = 56 + 4 = 60
Therefore, the total cost of the items in the currency "ANTI" (₳) in base 8 is ₳140 for rice and ₳60 for beans.