SOLUTION: Frank spent 1/7 of his money on shoes and 2/5 of the remaining amount on a shirt. How much money does he have left in terms of a fraction of the original amount?
Question 1209050: Frank spent 1/7 of his money on shoes and 2/5 of the remaining amount on a shirt. How much money does he have left in terms of a fraction of the original amount? Found 3 solutions by ikleyn, math_tutor2020, MathTherapy:Answer by ikleyn(52776) (Show Source):
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Frank spent 1/7 of his money on shoes and 2/5 of the remaining amount on a shirt.
How much money does he have left in terms of a fraction of the original amount?
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Frank spent
+ = + = + = of the original amount.
The fraction of money left is
- = - = = of the original amount. ANSWER
Solved.
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This problem is to solve it in one or two minutes, making standard transformations/calculations with fractions.
Its only goal is to give a student an opportunity to play/(to practice) with fractions.
All other explanations, including making plots and illustrations (as the other tutor does),
only DISTRACT from the true goal of this exercise.
Draw a grid of rectangles that are 7 units tall and 5 units across.
You can use graph paper or make your own grid.
Another approach is to take a screenshot of a blank excel spreadsheet so you can use it in something like MS Paint.
Shade the entire top row to represent Frank spending 1/7 of his starting money. You have shaded 1 row out of 7 rows total. The unshaded stuff is what he has left after buying the shoes (but he hasn't bought the shirt just yet). I'll represent this shading with a red X.
Then shade two entire columns (out of the 5 total columns) so we can depict Frank spending 2/5 of his remaining money. I'll represent this additional shading with a blue X. The unshaded blocks represent his remaining amount of money after buying the shoes and shirt.
The final unshaded region is 6 units tall and 3 units across.
There are 6*3 = 18 small rectangles in this unshaded region.
This is out of 7*5 = 35 original small rectangles.
18/35 is the final answer. The fraction cannot be reduced since 18 and 35 do not have any common factors other than 1.
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A non-visual method.
Frank spends 1/7 his money on shoes.
He has 1 - (1/7) = 6/7 of it remaining after buying the shoes.
Since he spends 2/5 of that on a shirt, he keeps 3/5 of that leftover portion.
(6/7)*(3/5) = (6*3)/(7*5) = 18/35
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An example
Let's say Frank starts with $350.
He spends (1/7)*350 = 50 dollars on shoes.
After buying the shoes, he would have 350-50 = 300 dollars.
(2/5)*300 = 120 dollars is spent on the shirt and his final leftover amount is 300-120 = 180 dollars.
Then 180/350 = (18*10)/(35*10) = 18/35 is the fractional amount he has compared to the starting $350.
Frank spent 1/7 of his money on shoes and 2/5 of the remaining amount on a shirt. How much money does he have left in terms of a fraction of the original amount?
Remainder after spending of INITIAL AMOUNT: =
Remainder after spending of REMAINDER: = =
(