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

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 lolli      Log On


   

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) About Me  (Show Source):
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[[[x}}}= total number of lollipos
J= number of lollipops Joe has
A= number of lollipops Amirah has
G= number of lollipops Gastle has
S= number of lollipops Sharifa has
"Joe, Amirah,Gastle and Sharifa had some lollipops" translates as
x=J%2BA%2BG%2BS .
"Joe had 5 lollipops less than 1/3 the total number of lollipops" translates as
J=%281%2F3%29x-5 .
"Amirah had 36 lollipops more than 1/3 the total number of lollipops" translates as
A=%281%2F3%29x%2B36 .
"Gastle had 1/5 the number of lollipops" translates as
G=%281%2F5%29J
"Sharifa had 5 lollipops less than Gastle" translates as
S=G-5 .
The whole problem translates as
.
It looks complicated, but everything can be expressed as a linear function of x .
---> ---> ---> ---> ---> ---> .
We are really only interested in the first equation. We will use the other ones just to verify the answer.
x=%281%2F3%29x-5%2B%281%2F3%29x%2B36%2B%281%2F15%29x-1%2B%281%2F15%29x-6
x=%281%2F3%29x%2B%281%2F3%29x%2B%281%2F15%29x%2B%281%2F15%29x%2B36-5-1-6
x=%282%2F3%29x%2B%282%2F15%29x%2B24
x=%2810%2F15%29x%2B%282%2F15%29x%2B24
x=%2812%2F15%29x%2B24
x=%284%2F5%29x%2B24
x-%284%2F5%29x=24
%281%2F5%29x=24
5%281%2F5%29x=5%2A24
highlight%28x=120%29

Let's verify by substituting x in the original equations:
Substituting x=120 we get
J=%281%2F5%29120-5=40-5=35 and
A=%281%2F5%29120%2B36=40%2B36=76 .
Substituting J=40 we get
G=%281%2F5%2935=7 .
Substituting G=8 we get
S=7-5=2 .
Now, substituting system%28J=35%2CA=76%2CG=7%2CS=2%29 into x=J%2BA%2BG%2BS we get
x=35%2B76%2B7%2B2=120 .
So, the calculations check, and highlight%28120%29 was the correctly calculated total number of lollipops.

Answer by MathTherapy(10552) About Me  (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: L%2F3+-+5

Amirah had: L%2F3+%2B+36

Gastle had: %281%2F5%29+%2A+%28L%2F3+-+5%29, or L%2F15+-+1

Sharifa had: L%2F15+-+1+-+5, or L%2F15+-+6

We then get: L%2F3+-+5+%2B+L%2F3+%2B+36+%2B+L%2F15+-+1+%2B+L%2F15+-+6+=+L

L%2F3+%2B+L%2F3+%2B+L%2F15+%2B+L%2F15+-+5+%2B+36+-+1+-+6+=+L

2L%2F3+%2B+2L%2F15+%2B+24+=+L

10L + 2L + 360 = 15L ------- Multiplying by LCD, 15

3L = 360

L, or number of lollipops = 360%2F3, or highlight_green%28120%29

Answer by ikleyn(52788) About Me  (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 %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.