The sum of a smaller number and a bigger number is 289. When the bigger number is divided by the smaller number, the quotient is 6 with the remainder 2. Find the two numbers.
- Smaller number
- Bigger number
(a)
Bigger number + Smaller number = Sum
Bigger number + Smaller number = 289
Bigger number ÷ Smaller number = Quotient with Remainder
Bigger number ÷ Smaller number = 6 with 2
Smaller number = Divisor
Bigger number = Dividend
Smaller number = 1 u
Bigger number
= Quotient x Divisor + Remainder
= 6 x 1 u + 2
= 6 u + 2
Total of the 2 numbers
= 6 u + 2 + 1 u
= 6 u + 1 u + 2
= 7 u + 2
7 u + 2 = 289
7 u = 289 - 2
7 u = 287
1 u = 287 ÷ 7 = 41
Smaller number
= 1 u
= 41
(b)
Bigger number
= 6 u + 2
= 6 x 41 + 2
= 248
Answer(s): (a) 41; (b) 248