Question 1208367: Hi
If Simon gave 30% of his sweets to Terry they will have the same number of sweets. If Simon gave 250 sweets to Terry, Terry will 80% more sweets than Simon. How many sweets does Simon have.
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
If Simon gave 30% of his sweets to Terry they will have the same number of sweets.
If Simon gave 250 sweets to Terry, Terry will 80% more sweets than Simon.
How many sweets does Simon have.
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x = # of Simon' sweets;
y = # of Terry' sweets.
From the problem, we have two equations.
First equation is
(1-0.3)x = y + 0.3x (first statement),
which simplifies to
0.7x = y + 0.3x ---> 0.7x - 0.3x = y ---> 0.4x = y.
Second equation is
x - 250 = = (y + 250) - 0.8*(x-250) (second statement),
which simplifies to
x - 250 = y + 250 - 0.8x + 200,
x - 250 - 250 - 200 = y - 0.8x
x - 700 = y - 0.8x
y = 1.8x - 700.
So, we have this system of two equations
y = 0.4x (1)
y = 1.8x - 700 (2)
Equations (1) and (2) have left sides identical, so their right sides are equal
0.4x = 1.8x - 700
700 = 1.4x
x = 700/1.4 = 500.
Thus Simon has 500 sweets.
From equation (1), Terry has 0.4*x = 0.4*500 = 200 sweets.
ANSWER. Simon has 500 sweets.
Solved.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Answer: 500
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.
| Scenario 1 | Before | After | | Simon | x | 0.7x | | Terry | y | y+0.3x |
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.
| Scenario 2 | Before | After | | Simon | x | x-250 | | Terry | y | y+250 |
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 = 500
Simon started with 500 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.
| Scenario 1 | Before | After | | Simon | 500 | 350 | | Terry | 200 | 350 |
Both end up with an equal number of candies (each with 350).
This confirms scenario 1.
| Scenario 2 | Before | After | | Simon | 500 | 250 | | Terry | 200 | 450 |
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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