SOLUTION: Hi Jenny distributed some pebbles to her friends . If she gave 6 pebbles to each friend she would be 2 pebbles short . If she 5 pebbles to each friend she would have 5 pebbles lef

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Question 1207244: Hi
Jenny distributed some pebbles to her friends . If she gave 6 pebbles to each friend she would be 2 pebbles short . If she 5 pebbles to each friend she would have 5 pebbles left. How many pebbles did she have in total.
Thanks
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Jenny distributed some pebbles to her friends.
If she gave 6 pebbles to each friend she would be 2 pebbles short.
If she 5 pebbles to each friend she would have 5 pebbles left.
How many pebbles did she have in total.
~~~~~~~~~~~~~~~~~~~~~~ 

Let P be the number of pebbles and let F be the number of friends.


Consider first statement "If she gave 6 pebbles to each friend she would be 2 pebbles short". 
It literally means that  

    P = 6F - 2.    (1)


Consider second statement "If she gave 5 pebbles to each friend she would be 5 pebbles left". 
It literally means that  

    P = 5F + 5.    (2)


Based on (1) and (2), we can write

    6F - 2 = 5F + 5.


It implies

    6F - 5F = 5 + 2

       F    =   7.


So, there are 7 friends to distribute pebbles.

From formula (1), the number of pebbles is  P = 6*7 - 2 = 42 - 2 = 40.

From formula (2), we get the same number of pebbles  P = 5*7 + 5 = 35 + 5 = 40.


ANSWER.  Jenny had 40 pebbles, in total.

Solved.



Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
i get that she had 7 friends and 40 pebbles.

here's how.

y = number of pebbles
x = number of friends.

if she gave 6 pebbles to each friend, she was 2 short leads to y - 6x = -2.
if she gave 5 pebbles to each friend, she had 5 left leads to y - 5x = 5.

subtract the second equation from the first to get 0 - x = -7.
solve for x to get x = 7.

when x = 7, y - 6x = -2 becomes y - 42 = -2.
solve for y to get y = 40.

replace y with 40 and x with 7 in both equations and you get:
40 - 42 = -2 and 40 - 35 = 5.

this confirms the values of x and y are true.

she had 7 friends and 40 pebbles.

your solution is that she had 40 pebbles in total.







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