Question 1208367
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Answer: <font color=red>500</font>


Explanation


x = number of sweets Simon starts with
y = number of sweets Terry starts with


Scenario 1. Simon gives 30% of his sweets to Terry. After this they end up with the same number of sweets.


Scenario 2. Simon gives 250 sweets to Terry. Afterward, Terry will have 80% more sweets compared to Simon.


<table border = "1" cellpadding = "5"><tr><td>Scenario 1</td><td>Before</td><td>After</td></tr><tr><td>Simon</td><td>x</td><td>0.7x</td></tr><tr><td>Terry</td><td>y</td><td>y+0.3x</td></tr></table>
Since they end up with the same number of sweets, we can say 0.7x = y+0.3x
Solve for y to get y = 0.4x
We'll use this later.


<table border = "1" cellpadding = "5"><tr><td>Scenario 2</td><td>Before</td><td>After</td></tr><tr><td>Simon</td><td>x</td><td>x-250</td></tr><tr><td>Terry</td><td>y</td><td>y+250</td></tr></table>
At the end of this scenario, Terry has 80% more sweets compared to Simon.
Think of it like this
TerrysCount = SimonsCount + 80% of SimonsCount
TerrysCount = SimonsCount + 0.8*SimonsCount
TerrysCount = (1 + 0.8)*SimonsCount
TerrysCount = 1.8*SimonsCount
Or think of "Terry has 80% more" as "Terry's count is 180% of Simon's count". 180% then converts to the decimal form 1.8


Based on that template, we can then say,
TerrysCount = 1.8*SimonsCount
y+250 = 1.8*(x-250)
0.4x+250 = 1.8*(x-250) .............. plug in y = 0.4x
0.4x+250 = 1.8x-450 
1.8x-0.4x = 250+450 
1.4x = 700
x = 700/1.4
x = <font color=red>500</font>
Simon started with <font color=red>500</font> sweets.
y = 0.4x = 0.4*500 = 200 is the number of sweets Terry started with.


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Let's check the answer. 
To do that we go through each scenario. 
I'll update each previous table to plug in the mentioned x and y values. 
<table border = "1" cellpadding = "5"><tr><td>Scenario 1</td><td>Before</td><td>After</td></tr><tr><td>Simon</td><td>500</td><td>350</td></tr><tr><td>Terry</td><td>200</td><td>350</td></tr></table>
Both end up with an equal number of candies (each with 350).
This confirms scenario 1.


<table border = "1" cellpadding = "5"><tr><td>Scenario 2</td><td>Before</td><td>After</td></tr><tr><td>Simon</td><td>500</td><td>250</td></tr><tr><td>Terry</td><td>200</td><td>450</td></tr></table>
Divide Terry's new count over Simon's new count to get 450/250 = 1.8 to show that Terry has 80% more compared to Simon.
Or you can notice that Terry has 450-250 = 200 more candies compared to Terry, and 200/250 = 0.80 = 80%


Both scenarios are confirmed. This confirms the answer.
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