Question

~ Joseph is twice as old as Allan (I get this its 2x assuming x is Allan's age) in five years allan's age will be two thirds of Joseph's age. how old are they now?
~the sum of the digits of a two digit number is 12. if the digits are reversed, the new number is 12 less than twice the original. find the new number.
~ the length of a rectangle is 4 less than twice its width. if the perimeter is at most 70 cm, find the biggest possible area of the rectangle.
** I have trouble interpreting word problems :(

Answer 1

words are always a problem; but its good to just take it piece by piece and construct a math sentence to match

Answer 2

Joseph is twice as old as Allan: j = 2a

in five years allan's age will be two thirds of Joseph's age

2(j+5)/3 = 2a + 5

how old are they now? with any luck i read that correctly ;)

Answer 3

we can say the j=2a or a=j/2; ima use a=j/2 and substitute it into the second part

2(j+5)/3 = 2a + 5

2(j+5)/3 = 2j/2 + 5

expand it all out to see it in a better light

2j/3 + 10/3 = j + 5

collect the js to one side and push everything else to the other side

2j/3 - j = 5 - 10/3

factor out a j

j (2/3 - 1) = 5 - 10/3

and divide of the extra

j = (5 - 10/3)/(2/3 - 1) = -5 .... what that tells me is that either my setup was incorrect, or j is very special :)

Answer 4

thank you!!! thank you!! at least I understand how this thing goes now :D I still have a bit of a problem translating word problems into equations though, but thanks!!

Answer 5

2(2a+5)/3 = 2a + 5

(4a+10)/3 = 2a + 5

a(4/3 - 2) = 5 - 10/3

a = (5 - 10/3)/(4/3 - 2) = -2.5

yeah, i still have issues with them as well .....

Answer 6

another way to approach this; is to consider that in 5 years, if we want to keep things as nice integers; in 5 years joseph has to be a multiple of 3

3 6 9 12 15; 15 looks kinda 5ish to me

15 - 5 = 10, and 10/2 is 5

j = 2a

10 = 2(5)

add 5 years

15 = 5.5.5; 10 = 5.5 which is 2/3 of it