SOLUTION: Patrick bought a bag of sweets. 3/8 of the sweets were apple-flavoured and the rest were strawberry-flavoured. After giving away 8/9 of the apple-flavoured sweets and 42 strawb

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Patrick bought a bag of sweets. 3/8 of the sweets were apple-flavoured and the rest were strawberry-flavoured. After giving away 8/9 of the apple-flavoured sweets and 42 strawb      Log On


   

Question 1188617: Patrick bought a bag of sweets.
3/8 of the sweets were apple-flavoured and the rest were
strawberry-flavoured.
After giving away 8/9 of the apple-flavoured sweets and 42
strawberry-flavoured sweets to his friends, he had 1/12 of the sweets
left.
Patrick paid $0.20 for each sweet.
How much did Patrick pay for the bag of sweets at first?
Found 4 solutions by Shin123, ankor@dixie-net.com, ikleyn, MathTherapy:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let's say there are 3x apple-flavored sweets and 5x strawberry-flavored sweets.
Once Patrick gives away 8/9 of the apple-flavored sweets, he has 3x%2A%281-8%2F9%29=3x%2A1%2F9=x%2F3 apple-flavored sweets left.
Patrick also gives away 42 strawberry-flavored sweets, so he has x%2F3 apple-flavored sweets and 5x-42 strawberry sweets left.
We are given that he has 1/12 of his sweets left after this and %283x%2B5x%29%2F12=2x%2F3. So we have x%2F3%2B5x-42=2x%2F3.
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=9.
  • Graphical form: Equation x%2F3%2B5x-42=2x%2F3 was fully solved.
  • Text form: x/3+5x-42=2x/3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2F3%2B5x-42=2x%2F3+%29
    For tutors: simplify_cartoon( x/3+5x-42=2x/3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+x%2F3+%29%2Bhighlight_red%28+5%2Ax+%29-42=2x%2F3.
Eliminated similar terms highlight_red%28+x%2F3+%29,highlight_red%28+5%2Ax+%29 replacing them with highlight_green%28+%281%2F3%2B5%29%2Ax+%29
It becomes highlight_green%28+%281%2F3%2B5%29%2Ax+%29-42=2x%2F3.
Look at %28highlight_red%28+1%2F3+%29%2Bhighlight_red%28+5+%29%29%2Ax-42=2x%2F3.
Added fractions or integers together
It becomes %28highlight_green%28+16%2F3+%29%29%2Ax-42=2x%2F3.
Look at highlight_red%28+%28highlight_red%28+16%2F3+%29%29%2Ax+%29-42=2x%2F3.
Remove unneeded parentheses around factor highlight_red%28+16+%29,highlight_red%28+1%2F3+%29
It becomes highlight_green%28+16+%29%2Fhighlight_green%28+3+%29%2Ax-42=2x%2F3.
Look at 16%2F3%2Ax-42=highlight_red%28+2%2Ax%2F3+%29.
Moved these terms to the left highlight_green%28+-2%2Ax%2F3+%29
It becomes 16%2F3%2Ax-42-highlight_green%28+2%2Ax%2F3+%29=0.
Look at 16%2F3%2Ax-highlight_red%28+42+%29-2%2Ax%2F3=0.
Moved -42 to the right of expression
It becomes 16%2F3%2Ax-2%2Ax%2F3-highlight_green%28+42+%29=0.
Look at highlight_red%28+16%2F3%2Ax+%29-highlight_red%28+2%2Ax%2F3+%29-42=0.
Eliminated similar terms highlight_red%28+16%2F3%2Ax+%29,highlight_red%28+-2%2Ax%2F3+%29 replacing them with highlight_green%28+%2816%2A1%2F3-2%2A1%2F3%29%2Ax+%29
It becomes highlight_green%28+%2816%2A1%2F3-2%2A1%2F3%29%2Ax+%29-42=0.
Look at %28highlight_red%28+16+%29%2Ahighlight_red%28+1+%29%2F3-2%2A1%2F3%29%2Ax-42=0.
Multiplied numerator integers
It becomes %28highlight_green%28+16+%29%2F3-2%2A1%2F3%29%2Ax-42=0.
Look at %2816%2F3-highlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2F3%29%2Ax-42=0.
Multiplied numerator integers
It becomes %2816%2F3-highlight_green%28+2+%29%2F3%29%2Ax-42=0.
Look at %28highlight_red%28+16%2F3+%29-highlight_red%28+2%2F3+%29%29%2Ax-42=0.
Added fractions or integers together
It becomes %28highlight_green%28+14%2F3+%29%29%2Ax-42=0.
Look at highlight_red%28+%28highlight_red%28+14%2F3+%29%29%2Ax+%29-42=0.
Remove unneeded parentheses around factor highlight_red%28+14+%29,highlight_red%28+1%2F3+%29
It becomes highlight_green%28+14+%29%2Fhighlight_green%28+3+%29%2Ax-42=0.
Look at highlight_red%28+14%2F3%2Ax-42+%29=0.
Solved linear equation highlight_red%28+14%2F3%2Ax-42=0+%29 equivalent to 4.66666666666667*x-42 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=9.

Universal Simplifier and Solver


Done!

Since x=9, there were 9%2A8=72 sweets at the beginning, so it cost Patrick $0.20*72=$14.40.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Patrick bought a bag of sweets.
let s = original number of sweet
3/8 of the sweets were apple-flavoured and the rest were strawberry-flavoured.
3%2F8s = no. of apple flavored
5%2F8s = no. of strawberry flavored
:
After giving away 8/9 of the apple-flavoured sweets and 42 strawberry-flavoured
sweets to his friends, he had 1/12 of the sweets left.
he had (1/9)s left therefore
(1%2F9*3%2F8s) + (5%2F8s - 42) = 1%2F12s
3%2F72s + 5%2F8s = 1%2F12s + 42
Common denominator is 24, rearrange to:
1%2F24 + 15%2F24 - 2%2F24 = 42
14%2F24s = 42
get rid of the denominator, multiply b 24
14s = 1008
s = 1008/14
s = 72 sweets originally
:
Patrick paid $0.20 for each sweet.
How much did Patrick pay for the bag of sweets at first?
72 * .20 = $14.40
:

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

If I be a student,  I would pay money back for only one single purpose that nobody
teaches me in this way as this pluggable solver does.


//////////////


My sincere advise to all future readers of this group of posts:

        do not take seriously the solution produced by a pluggable solver:
        do not spend your time on it . . .



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Patrick bought a bag of sweets.
3/8 of the sweets were apple-flavoured and the rest were
strawberry-flavoured.
After giving away 8/9 of the apple-flavoured sweets and 42
strawberry-flavoured sweets to his friends, he had 1/12 of the sweets
left.
Patrick paid $0.20 for each sweet.
How much did Patrick pay for the bag of sweets at first?
The pluggable "gadget" is extremely inefficient and does not serve any purpose in teaching someone
to solve a problem. I guess to some it's cute and entertaining! And, I believe it's a lazy person's tool.

Let multiplicative factor for original number of sweets be x
Then original numbers of apple-flavored and strawberry-flavored sweets are: 3x and 5x, respectively
Then total number of sweets = 3x + 5x = 8x
After 8%2F9 of the apple-flavored are given away, matrix%281%2C5%2C+1%2F9%2C+of%2C+3x%2C+or%2C+x%2F3%29 remain
After 42 of the strawberry-flavored are given away, 5x - 42 remain
Since 1%2F12 of the total number of sweets remain, we get: 
x + 15x - 126 = 2x ---- Multiplying by LCD, 3
        - 126 = 2x - 16x
        - 126 = - 14x
Multiplicative factor for original number of sweets, or matrix%281%2C5%2C+x%2C+%22=%22%2C+%28-+126%29%2F%28-+14%29%2C+%22=%22%2C+9%29
Original number of sweets: highlight_green%28matrix%281%2C3%2C+8%289%29%2C+%22=%22%2C+72%29%29

Cost of original 72 sweets, at $0.20 per sweet:  72(.20) = $14.40