Question 1203368: Hi
Irene bought 10 pens with 2/5 of her money. If she bought another 24 pens then she would need $18 more. What is the amount of money she had left after buying the 10 pens.
Thanks
Found 5 solutions by josgarithmetic, ikleyn, math_tutor2020, MathTherapy, greenestamps:
Answer by josgarithmetic(39623)   (Show Source):
Answer by ikleyn(52839)  (Show Source):
You can put this solution on YOUR website! .
Irene bought 10 pens with 2/5 of her money. If she bought another 24 pens then she would need $18 more.
What is the amount of money she had left after buying the 10 pens.
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Such problems on "shortage the money" are traditionally considered
as entertainment Math problems.
Therefore, I will give you MENTAL solution below.
Since Irene bought 10 pens with 2/5 of her money, it means that
she could buy 15 more pens for her remaining 3/5 of money.
But the problem said that if she bought additional 24 pens (additional to that 10 pens),
she would be $18 short.
It means that 24-15 = 9 extra pens cost $18. Hence, each pen costs 18/9 = 2 dollars.
Great (!) Half of the problem is solved. The rest is just easy.
One pen costs 2 dollars; hence, 15 pens cost 30 dollars,
and it is the amount of money she had left after buying the 10 pens.
ANSWER. After buying 10 pens, Irene had left 30 dollars.
Solved.
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The solution by @josgarithmetic is incorrect, as usual.
Therefore, for the peace in your mind and for safety of your mind, ignore his post.
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!
Answer: $30
Work Shown
m = amount of starting money
(2/5)m = cost of 10 pens
(3/5)m = amount of money left over
(3/5)m+18 = amount of money needed to buy 24 more pens
(2/5)m = cost of 10 pens
(1/10)*(2/5)m = (1/25)m = cost of 1 pen
(24/25)m = cost of 24 pens
(3/5)m+18 = (24/25)m
25* [ (3/5)m+18 ] = 25*(24/25)m
15m+450 = 24m
450 = 24m-15m
450 = 9m
m = 450/9
m = 50
Irene started with $50
2/5 of this is (2/5)*50 = 20 dollars
10 pens = $20 ---> 1 pen = 20/10 = 2 dollars
Another 24 pens will cost 2*24 = 48 additional dollars, but Irene has 50-20 = 30 dollars remaining.
She needs 48-30 = 18 extra dollars. This helps us confirm the answer.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website!
He's still WRONG! Price of 1 pen is NOT $18, and NOT $0.75. Her initial amount of money is NOT $18.75,
and amount remaining after buying 10 pens DEFINITELY isn't $11.25.
Doesn't he realize that 2 others did the problem and got remaining amount after the purchase, as $30?
Let me add my "piece."
Let original amount she had, be A
Since she bought 10 pens with  of her money, she spent  on 10 pens.
Therefore, each pen costs: 
Buying another 24 pens would cost her 
Therefore, 34 (10 + 24) pens cost 
Since she’d need $18 more to buy the extra 24 pens, we get: 
34A = 25A + 18(25) ---- Multiplying by LCD, 25
34A - 25A = 18(25)
9A = 18(25)
Original amount she had, or: 
After using of her money to buy the 10 pens, she had  remaining, or 
Answer by greenestamps(13203)  (Show Source):
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