SOLUTION: Joe,Amirah,Gastle and Sharifa had some lollipops .Joe had 5 lollipops less than 1/3 the total number of lollipops .Amirah had 36 lollipops more than 1/3 the total number of lollipo

Algebra ->  Finance -> SOLUTION: Joe,Amirah,Gastle and Sharifa had some lollipops .Joe had 5 lollipops less than 1/3 the total number of lollipops .Amirah had 36 lollipops more than 1/3 the total number of lollipo      Log On


   

Question 1044253: Joe,Amirah,Gastle and Sharifa had some lollipops .Joe had 5 lollipops less than 1/3 the total number of lollipops .Amirah had 36 lollipops more than 1/3 the total number of lollipops .Gastle had 1/5 the number of lollipops Joe had and Sharifa had 5lollipops less than Gastle .How many lollipops were there in total?
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Joe,Amirah,Gastle and Sharifa had some lollipops .Joe had 5 lollipops less than 1/3 the total number of lollipops.
Amirah had 36 lollipops more than 1/3 the total number of lollipops .Gastle had 1/5 the number of lollipops Joe had
and Sharifa had 5 lollipops less than Gastle. How many lollipops were there in total?
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Let x be one third of the total number of lollipops.

Then Joe had x - 5 lollipops.

Then Amirah had x + 36 lollipops.

Gastle had %28x-5%29%2F5 lollipops.

Sharifa had %28x-5%29%2F5+-+5 lollilops.

The equation is:

Joe + Amira + Gastle + Sharifa = 3x,   or

(x-5) + (x+36) + %28x-5%29%2F5 + %28x-5%29%2F5+-+5 = 3x.

Multiply both sides by 5. You will get

5x - 25 + 5x + 180 + x-5 + x-5 - 25 = 15x,   or

12x + 120 = 15x,

3x = 120. 

It is exactly what the problem is asking for.

Answer.  120 lollipops.