121 balls are placed in group of 7and 5 in basket.how many baskets 0f 7 were there?
An obvious solution would be
7*3+5*20=121
Consequently, change 5*7 for 7*5 gives
7*(3+5)+5*(20-7)=7*8+5*13=121
Similarly,
7*(8+5)+5*(13-7)=7*13+5*6=121
We cannot go further because number of baskets for groups of 5 will be negative.
So possible values for baskets of 7 are:
3,8,13
To determine how many baskets of 7 balls there were, we need to divide the total number of balls (121) by 7.
Using the division method, we divide 121 by 7:
- Divide 7 into the first digit of 121 (which is 1). Since 7 cannot be divided into 1, we carry over the next digit (2), making it 12.
- Divide 7 into 12. 7 goes into 12 once, resulting in 7. The remainder is 5.
- Bring down the next digit (1) to the remainder. So, we have 51.
- Divide 7 into 51. 7 goes into 51 seven times, resulting in 49. The remainder is 2.
- Since there are no more digits to bring down, we have completed the division.
Therefore, there are 17 baskets of 7 balls in a total of 121 balls.