A shopkeeper had 410 tangerines. He put some of them into 15 cartons containing 12 tangerines each. He then put the rest into 14 cartons, each containing the same number of tangerines.
(a) How many tangerines were in each of the 14 cartons?
(b) How many tangerines were left?
15*14 + 14*x = 410
x = 200/14 = 14 4/14 <===== 14*14 + 4 = 200
make use of this bit of arithmetic
To find the answers, we will solve the problem step by step.
(a) To find how many tangerines were in each of the 14 cartons, we first need to calculate the total number of tangerines placed in the 15 cartons.
The number of tangerines in the 15 cartons = Total number of cartons * Number of tangerines per carton.
Number of tangerines in the 15 cartons = 15 * 12 = 180.
Now, we can find the number of tangerines placed in the remaining 14 cartons by subtracting the tangerines in the 15 cartons from the total number of tangerines.
Number of tangerines in the remaining 14 cartons = Total number of tangerines - Number of tangerines in the 15 cartons.
Number of tangerines in the remaining 14 cartons = 410 - 180 = 230.
To find the number of tangerines in each of the 14 cartons, we divide the remaining tangerines by the number of cartons.
Number of tangerines in each of the 14 cartons = Number of tangerines in the remaining 14 cartons / Number of cartons.
Number of tangerines in each of the 14 cartons = 230 / 14 ≈ 16.43.
Rounded to the nearest whole number, each of the 14 cartons contains approximately 16 tangerines.
(b) To find the number of tangerines left, we subtract the tangerines put in the cartons from the total number of tangerines.
Number of tangerines left = Total number of tangerines - Number of tangerines in the cartons.
Number of tangerines left = 410 - (Number of tangerines in the 15 cartons + Number of tangerines in the 14 cartons).
Number of tangerines left = 410 - (180 + (14 * 16)).
Number of tangerines left = 410 - (180 + 224).
Number of tangerines left = 410 - 404 = 6.
Therefore, there were 16 tangerines in each of the 14 cartons, and 6 tangerines were left.
To answer these questions, we can make use of basic arithmetic and algebraic concepts. Let's break it down step by step:
(a) To find out how many tangerines were in each of the 14 cartons, we need to determine how many tangerines were left after filling the first 15 cartons.
The first 15 cartons contain a total of 15 cartons * 12 tangerines/carton = 180 tangerines.
Therefore, the remaining number of tangerines is 410 tangerines - 180 tangerines = 230 tangerines.
Since these 230 tangerines are divided equally among the 14 remaining cartons, we can calculate the number of tangerines in each carton by dividing the total number of tangerines by the number of cartons: 230 tangerines ÷ 14 cartons ≈ 16.43 tangerines.
Since we can't have a fraction of a tangerine, we need to round it to the nearest whole number. Thus, each of the 14 cartons would have approximately 16 tangerines.
(b) To calculate the number of tangerines left, we need to subtract the total number of tangerines put into the cartons from the initial number of tangerines.
We already know that the first 15 cartons contain 180 tangerines. Adding the tangerines in the 14 cartons (14 cartons * 16 tangerines/carton = 224 tangerines), we get a total of 180 tangerines + 224 tangerines = 404 tangerines.
To find the number of tangerines left, we subtract this total from the initial number of tangerines: 410 tangerines - 404 tangerines = 6 tangerines.
Therefore, there are 6 tangerines left over.
In summary:
(a) Each of the 14 cartons would contain approximately 16 tangerines.
(b) There are 6 tangerines left.