Question

1,406 candies are packed in a box of 6 candies. Each remaining candy is divided among the boxes. So, a few boxes have 6 candies and the rest have 7 candies.

Calculate the values of $x$ and $y$ in the following:

• A. $x$ = 223
  $y$ = 2
• B. $x$ = 245
  $y$ = 3
• C. $x$ = 267
  $y$ = 3
• D. $x$ = 232
  $y$ = 2

Answer 1

The correct option is D $x$ = 232

$y$ = 2
Total number of candies = 1,406
Number of candies in a box = 6

To determine the number of boxes with 6 candies and 7 candies, we have to calculate 1406 $÷$ 6 and find the remainder.

Let us solve this through partial quotient method.

First, we write the values in the long division bracket.


Now, we find an easier multiple of the divisor, 6, which is closer to the dividend 1,406.


We subtract the easier multiple 1,200 from the dividend 1,406 and write the partial quotients in the right column.


Let's keep repeating the process until the dividend is reduced to zero or the remainder is less than the divisor.


Now, we add all the partial quotients.

Final quotient = 200 + 30 + 4 = 234
Remainder = 2

Now, the number of boxes with 6 candies each is 234 and we have 2 remaining candies.

Let's distribute 2 candies in the box of 6 candies each.

Now, we have 2 boxes with 7 candies each.

∴ Number of boxes with 6 candies = 234 - 2 = 232