ElectricPavlov

Pick two convenient points   0,4    and    1,1

slope = (y1-y2) / (x1-x2)    =    3/-1 = -3  = m

b is when x = 0    in this graph  b= 4

y = mx+b    becomes

y = -3x +4

NOW   m = 4s

 in three years they will BOTH be +3 years

m+3 = 3(s+3)      sub in m = 4s

4s + 3 = 3s+9

s = 6    m = 24 y/o

I count 14 ....  anyone else?   (edited)

No...I mean START with the LCM 60   and count backwards ....first one with a 5 remainder when divided by 6 is        59    

Slope intercept form   is    y = mx + b     m = slope   b = y intercept (value when x = 0)

y = -1/2 x + b     now put in the point given to calculate 'b'

-4 = -1/2(-3) + b      so b = -5 1/2

y = -1/2x  - 5 1/2

Point slope form :

y − y1 = m(x − x1)       sub in the point given

y - -4  = -1/2(x - -3)

y+4 = -1/2(x+3)

3/10(t+2)-t/20>-3/5       multiply both sides of the equation by 20 to get:

6 (t+2) - t > -12

6t+12-t>-12            simplify ....and subtract 12 from both sides

5t > -24

t > -24/5

MAYBE go backwards from the LCM       LCM  4 5 6 = 60        I do not know if that always works !

That is the method I used the othe day while solving one of these....it might be a little shorter to arrive at the number if you start with the largest divisor in the question: '6 '  with remainder 5

11   23    29   35    41   47    53    59   

I do not know an eaiser (or another) way to solve these.....maybe something with the modulo function (of which I am not very familiar)....

   Let me know if you find the true 'mathematical way' !     ~ EP  

Similar triangles

10 is to 6 as     ? is to 15

10/6 = ?/15     solve for ?     (mutiply both sides of the equation by 15)

Anyone ever tell you that you are rather impolite and demanding?  They should.....

1-9   is 9 digits

10 - 99  is 180 more digits      total so far 189

187   would be  in  '98'     as in '8'      188 would be the first '9' in page  99