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 lolli

Question 1044345: 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?
Found 3 solutions by KMST, MathTherapy, ikleyn:
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
[[[x}}}= total number of lollipos
= number of lollipops Joe has
= number of lollipops Amirah has
= number of lollipops Gastle has
= number of lollipops Sharifa has
"Joe, Amirah,Gastle and Sharifa had some lollipops" translates as
.
"Joe had 5 lollipops less than 1/3 the total number of lollipops" translates as
.
"Amirah had 36 lollipops more than 1/3 the total number of lollipops" translates as
.
"Gastle had 1/5 the number of lollipops" translates as

"Sharifa had 5 lollipops less than Gastle" translates as
.
The whole problem translates as
.
It looks complicated, but everything can be expressed as a linear function of .
---> ---> ---> ---> ---> ---> .
We are really only interested in the first equation. We will use the other ones just to verify the answer.

Let's verify by substituting in the original equations:
Substituting we get
and
.
Substituting we get
.
Substituting we get
.
Now, substituting into we get
.
So, the calculations check, and was the correctly calculated total number of lollipops.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

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?

Let number of lollipops be L
Then Joe had:
Amirah had:
Gastle had: , or
Sharifa had: , or
We then get:

10L + 2L + 360 = 15L ------- Multiplying by LCD, 15
3L = 360
L, or number of lollipops = , or
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~

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 lollipops. Sharifa had lollilops. The equation is: Joe + Amira + Gastle + Sharifa = 3x, or (x-5) + (x+36) + + = 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.

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