SOLUTION: Sandy had some apples and Pears. After selling 1/3 of the apples and 7 pears, the number of pears left was a quarter of the number of apples left. If the number of pears sold was 1

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Question 1164369: Sandy had some apples and Pears. After selling 1/3 of the apples and 7 pears, the number of pears left was a quarter of the number of apples left. If the number of pears sold was 1/6 the number of the pears that were not sold, how many pears did Sandy have at first??
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
sandy had x apples and y pears.
x = number of apples.
y = number of pears.

she sold 1/3 * x apples and 7 pears.
she had 2/3 * x apples and y - 7 pears left.

the number of pears that were left was 1/4 of the number of apples that were left.
y - 7 = 1/4 * 2/3 * x = 1/6 * x

the number of pears sold was 1/6 * the number of pears that were not sold.
7 = 1/6 * 1/6 * x = 1/36 * x
solve for x to get x = 7 * 36 = 252.
you have:
x = 252

since the number of pears that were not sold is equal to 1/6 * x, then the number of pears not sold is equal to 1/6 * 252 = 42
you have y - 7 = 42
solve for y to get y = 42 + 7 = 49
you have:
y = 49

x = 252 and y = 49 means she had 252 apples at first and 49 pears at first.

to confirm, go through the problem again with 252 apples and 49 pears.
she sold 1/3 of the apples and 7 of the pears.
that means she sold 84 apples and 7 pears.
252 - 84 = 168 apples left.
49 - 2 = 42 pears left.
the number of pears left was 1/4 of the number of apples left.
42 = 1/4 * 168 becomes 42 = 42, confirming this is correct.
the number of pears sold was 1/6 times the number of pears that were not sold.
7 pears were sold.
1/6 * 42 = 7, confirming this is correct.

the solution looks good.
the solution is that she had 49 pears at first.


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
Sandy had some apples and Pears. After selling 1/3 of the apples and 7 pears, the number of pears left was a quarter of the number of apples left. If the number of pears sold was 1/6 the number of the pears that were not sold, how many pears did Sandy have at first??
All the mumbo-jumbo is NOT needed, unless other questions are asked. If this is the only question associated with the problem, then ALL that’s needed is: 
Sandy had some apples and  pears. After selling 1/3 of the apples and 7 pears, the number of pears left was a quarter of the number of apples left. If the number of pears sold was 1/6 the number of the pears that were not sold, how many pears did Sandy have at first??

Let original number of pears Sandy had, be P
After selling 7 pears, she had P - 7 pears left
With number of pears sold being  of unsold pears, we have:  
42 = P  -  7 ------ Multiplying by LCD, 6 
42 + 7 = P
Original number of pears, or 
That's ALL! 
There's ABSOLUTELY nothing else that you need to do! Doing anything else is totally unnecessary unless you have time to waste!
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