Two positive integers are in the ratio of 7:2. If 3 is added to each and the larger of the resulting numbers is then divided by the smaller of the resulting numbers, the quotient is 2 and the remainder is 12. Find the larger of the original numbers.
2007-01-19 09:50:41 · 6 answers · asked by SallyJane 3 in Science & Mathematics ➔ Mathematics
x=35, y = 10
I did it by trial and error using multiples of 7 and 2 though there is probably an easier way
x/y=7/2
now we need to find an (x+3)/(y+3)= 2 with a remainder of 12
so i tried 7 and 2 first and got (7+3)/(2+3)= 10/5=2
14 and 4 makes (14+3)/(4+3) = 17/7 = 2 with remainder 3
and so on until i tried 35 and 10
(35+3)/(10+3)=38/13= 2 12/13 or 2 with 12 remainder
2007-01-19 10:01:01 · answer #1 · answered by Bill F 6 · 0⤊ 0⤋
35 is the larger number and 10 is the smaller number. 35+3=38. 10+3=13
1 x 13 = 13
2 x 13 = 26
38 - 26 = 12
38 / 13 = 2 remainder 12
2007-01-19 09:59:32 · answer #2 · answered by Quaterno 1 · 0⤊ 0⤋
unknown: x and y
known: 2*x=7*y
(x+3)/(y+3)=2 +12/(y+3) or x+3=2*y+6+12=>x=2*y+15
=>x=2*(2*x/7)+15=>x=4*x/7+15
=>3*x/7=15=>x=35=>y=10
2007-01-19 10:00:54 · answer #3 · answered by iron_pennywise 1 · 0⤊ 0⤋
35
2007-01-19 10:03:00 · answer #4 · answered by Crunchy_Crunchy 1 · 0⤊ 0⤋
35
7x/2x will always have a ratio of 7/2
7x+3/2x+3 = 2 + 12/2x+3
mulyiply both sides by 2x + 3
7x+3 = 4x + 6 + 12
3x = 15
x = 5
7*5 = 35
2007-01-19 09:58:23 · answer #5 · answered by trichbopper 4 · 1⤊ 0⤋
7x+3
____ = 2x+12
2x+3
use the formula
2007-01-19 10:07:04 · answer #6 · answered by Dosage 3 · 0⤊ 0⤋