hi can you help me with this question grandpa wants to share his money among his grandsons if he gives them 30,000 each one he will be left with 60000, if he gives them 50,000 he will need an additional 100,000. how much money grandpa wishes to share among his grandsons?

Question

hi can you help me with this question  grandpa wants to share his money among his grandsons if he gives them 30,000 each one he will be left with 60000, if he gives them 50,000 he will need an additional 100,000.   how much money grandpa wishes to share among his grandsons?

hoblos · Answer

let's suppose first that the total money is y
and the number of grandsons is x

so we need to translate the given to a system of 2 equations with 2 unknowns x & y

anonymous · Answer

Is it how much money he wants to spend if he gives them 30,000 each or if he gives them 50,000 each?

hoblos · Answer

"if he gives them 30,000 each one he will be left with 60000"
 this means that if he gives each of the x grandsons 30000 , he would pay y-60000                         
so           30000x = y - 60000

this is the first equation

can you fibd the secod one ?

anonymous · Answer

hey hoblos i see

anonymous · Answer

But the grandpa has 8 grandsons. Because if he gives them each 30,000, he will have 60,000 left and once he gives 50,000 each, he needs 100,000 more. So, a 20,000 increase per person means that there is an increase of 160,000. And 160,000/20,000 = 8.

anonymous · Answer

i dont get why that ecuation has both incognites on it

anonymous · Answer

hey so it woulb be something like this 50,000x = y + 100,000

anonymous · Answer

for the second ecuation

hoblos · Answer

yeah you are right,
now you have to solve the system

anonymous · Answer

ok so this is the system

anonymous · Answer

30,000x = y - 60,000
50,000x = y + 100,000

hoblos · Answer

yep this is it,
do you know how to solve it ?

anonymous · Answer

i dont quite remember.

hoblos · Answer

solve one of the 2 equations for y, then replace it in the other and solve for x

anonymous · Answer

so i have to rearrange the equations like this 
y=30,000x + 60,000
y=50,000x - 100,000

hoblos · Answer

yeah
now set y=y
and solve for x

anonymous · Answer

so 30,000x + 60,000 = 50,000x - 100,000

hoblos · Answer

correct

anonymous · Answer

30,000x - 50,000x = -60,000-100,000
20,000x = -160,000
x= -80,000   

i got this but im getting a negative value is that right

hoblos · Answer

|dw:1396210335372:dw|

hoblos · Answer

there must be a "-" there

anonymous · Answer

oh my friend thanks for pointing that out :)

hoblos · Answer

so  we get 
20,000x = -160,000

now divide both sides by 20,000

anonymous · Answer

so yeah answer is 300,000 thanks my friend.

hoblos · Answer

yeah your answer is correct
good work

anonymous · Answer

i really helped me knowing which were the things i was being asked money=y and grandsons=x

anonymous · Answer

Thank you so much.

hoblos · Answer

glad to help! :)