find the sum of all two digit positive numbers which when divided by 7 yield 2 and 5 as remainder
Answers
Answer:
The sum of all two digit positive numbers is 19.
Step-by-step explanation:
Let x be the two digit positive number
x/7 = 2 + 5/7 Since 5 is the remainder and the divisor is 7, it should be 5/7.
x/7 = 14/7 + 5/7 Add the whole number 2 and the fraction 5/7 by finding its LCD (Least Common Denominator)
x/7 = 19/7 Apply cross-multiplication.
7(x) = 7(19) Multiply.
7x = 423 Apply DPE (Division Property of Equality).
7x/7 = 423/7 Divide both sides by 7 applying DPE (Division Property of Equality).
x = 19
Since there are no other values of x, then, the sum of all two digit numbers which when divided by 7 yield 2 and 5 as a remainder is 19.
Checking:
19/7 = 2 remainder 5
Answer:
The sum of all two digit positive numbers which when divided by 7 yield 2 and 5 as remainder will be 1372
Step-by-step explanation:
The numbers that will give remainder as 2 and 5 when dividd by 7 can be given by the relation,
y = 7x + 2 or y = 7x + 5 where x can be 0,1,2 .....14
hence their sum can be given by,
S = ∑(7x + 2) + ∑(7x + 5) where x can be 0,1,2 .....13
= [ 2 + 9 + 16 + 23 + 30 + 37 + 44 + 51 + 58 + 65 + 72 + 79 + 86 + 93] + [ 5 + 12 + 19 + 26 + 33 + 40 + 47 + 54 + 61 + 68 + 75 + 82 + 89 + 96 ]
= 665 + 707
= 1372
Hence the sum of all two digit positive numbers which when divided by 7 yield 2 and 5 as remainder will be 1372