Answer:
Smaller Amount =$206
Larger Amount =$309
Step-by-step explanation:
Let the total amount of money =x
The money will be divided in the ratio 2:3
Total Number of Shares =2+3=5
Therefore:
Smaller Amount [tex]=\dfrac25x[/tex]
Larger Amount[tex]=\dfrac35x[/tex]
Four times the smaller amount is one hundred three dollars less than three times the larger amount.
Therefore:
[tex]3$ X\dfrac35x=4$ X \dfrac25x + 103\\\dfrac{9x}{5}=\dfrac{8x}{5}+103\\$Collect like terms\\\dfrac{9x}{5}-\dfrac{8x}{5}=103\\\dfrac{x}{5}=103\\$Cross multiply\\x=103*5\\Amount of money to be shared, x=\$515[/tex]
Therefore:
Smaller Amount [tex]=\dfrac25$ X 515 =\$206\\[/tex]
Larger Amount[tex]=\dfrac35$ X 515 =\$309[/tex]
The largest amount will be $300
Let the smaller amount be "x"
Let the larger amount be "y"
If the money will be divided in the ratio of 2 to 3, then x: y = 2:3
If four times the smaller amount is one hundred three dollars less than three times the larger amount, this is expressed as:
4x = 3y - 100 ...... 1
Since x/y = 2/3
3x = 2y
x = 2y/3 ...... 2
Substitute equation 2 into 1 to have:
4x = 3y - 100
4(2y/3) = 3y - 100
8y/3 = 3y - 100
8y/3 - 3y = -100
(8y-9y)/3 = -100
-y = -300
y = 300
Since x = 2y/3
x = 2(300)/3
x = 600/3
x = 200
Hence the largest amount will be $300
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