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EXOEXOEXO
 one year ago
andy had 20% fewer marbles than henry. when andy gave 80 marbles to henry, the number of marbles he had left was half of what henry had. how many marbles did andy have in the beginning?
EXOEXOEXO
 one year ago
andy had 20% fewer marbles than henry. when andy gave 80 marbles to henry, the number of marbles he had left was half of what henry had. how many marbles did andy have in the beginning?

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Let's say originally Henry had x marbles. Then Andy originally has 20% fewer marbles than x. How do you write mathematically 20% fewer than x?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Correct. We have this: Originally After Giving Henry x Andy 0.8x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Now we need to figure out what the numbers are after giving.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Correct. Originally After Giving Henry x x + 80 Andy 0.8x 0.8x  80 After giving the marbles, Andy had 0.8x  80 marbles. From the given, we know Andy had 0.5x left, so 0.8x  80 = 0.5x

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Remember that we started above by letting x = number of marbles Henry had originally. If you solve the last equation above for x, that will tell you how many marbles Henry had originally. Then 0.8x is how many marbles Andy had originally.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Ok. we see there is a problem. I get 266.6666...

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2The number of marbles must be a whole number. When I read the problem I noticed there is a sentence that can be interpreted two ways. We interpreted one way and got 266.666... marbles. Let's interpret the sentence the other way and see what we get. I'll show you which sentence I am referring to below.

Mertsj
 one year ago
Best ResponseYou've already chosen the best response.0I believe that .8x80=1/2(x+80)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2This is how we interpreted the question. I am adding words in square brackets to show our original interpretation. [Originally] Andy had 20% fewer marbles than Henry. When Andy gave 80 marbles to Henry, the number of marbles he had left was half of what Henry had [before Henry was given the extra marbles]. How many marbles did Andy have in the beginning?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2This is the other way to interpret the question. I am adding words in square brackets to show our original interpretation. [Originally] Andy had 20% fewer marbles than Henry. When Andy gave 80 marbles to Henry, the number of marbles he had left was half of what Henry had [***after*** Henry was given the extra marbles]. How many marbles did Andy have in the beginning?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Since with the second interpretation, we need to deal with Henry's marbles after he got the extra 80 marbles from Andy, then the number of marbles Andy has in the end is equal to 0.5(x + 80) That gives us the new equation: 0.8x  80 = 0.5(x + 80)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2If we solve the new equation, we get x = 400, which is a whole number and makes more sense.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2If Henry had 400 marbles originally, then Andy had 0.8(400) marbles originally.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.2Yes, you got it. Good job!
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