Here are the 2-digit-multiples of 8:
16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96
Which of those has digits that add up to 10?
name the 2 digit multiple of 8 who digits add up to 10
3 answers
If you are seeking an algebraic approach:
1--8x = 10A + B
2--A + B = 10
3--8x = 10A + 10 - A
4--8x = 9A + 10
5--8x - 9A = 10
6--Dividing by the lowest coefficient, yields x - A - A/8 = 1 + 2/8
7--(A + 2)/8 must be an integer k making A = 8k - 2
8--Substituting back into (4) yields x = 9k - 1
9--Clearly, k can only be 1 as k = 0 yields negative results and k = 2 or more yields 2 digit values for A and B.
10--Thus, for k = 1, x = 8, A = 6 and B = 4 yielding 8(8) = 64 where 6 + 4 = 10.
1--8x = 10A + B
2--A + B = 10
3--8x = 10A + 10 - A
4--8x = 9A + 10
5--8x - 9A = 10
6--Dividing by the lowest coefficient, yields x - A - A/8 = 1 + 2/8
7--(A + 2)/8 must be an integer k making A = 8k - 2
8--Substituting back into (4) yields x = 9k - 1
9--Clearly, k can only be 1 as k = 0 yields negative results and k = 2 or more yields 2 digit values for A and B.
10--Thus, for k = 1, x = 8, A = 6 and B = 4 yielding 8(8) = 64 where 6 + 4 = 10.
Name the 2 digit multiple of 8 whose digits add up to 10
1 answer