SOLUTION: Natalie went to the movies for $16.50 then spent half of her remaining money on jogging shoes. Next she bought lunch for $9.00 then spent half her remaining money on a skirt. After
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Question 982654: Natalie went to the movies for $16.50 then spent half of her remaining money on jogging shoes. Next she bought lunch for $9.00 then spent half her remaining money on a skirt. After that she still had $21 left. How much money did she start with?
I tried 21 x 2 = 42
42 + 9 = 51
51 x 2 = 102
102 + 16.50 = 118.50
So she started with $118.50 but I'm not sure if this is the correct way of doing it.
Answer by josgarithmetic(39626) (Show Source): You can put this solution on YOUR website!
Calculate one step at a time in the sequence of spending events.
Amount of original money she had, give a variable: p, the amount of money at start.
went to the movies for $16.50 then spent half of her remaining money on jogging shoes.
She now had dollars.
OR
Next she bought lunch for $9.00
Her money not yet spent is dollars.
OR
...then spent half her remaining money on a skirt.
She then still had ,
and this quantity she still had is stated to be $21.
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OR if updating as you go,
Calculated? Maybe. Simplified? Not yet. Simplify the expression on the right, and then solve for p.
... Another idea, is multiply left and right sides by 2, simplify from that step; and multiply left and right sides AGAIN by 2, simplify and then solve for p. Why this way, is because you want to handle the complex fractions carefully.
Still another way is to go back and simplify each stage of the process, but this may be more difficult to manage.
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Still not sure? Go back and work through each step of the spending process one at a time, in sequence!
I supplied the "calculate as you go" results. I will not place all the algebra steps here because the text is fairly difficult to type through a keyboard in contrast to being somewhat less difficult to do on paper. You would then solve the "21" equation for p.
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My final result:
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