Some money will be divided in the ratio of 2 to 3. Four times the smaller amount is one hundred three dollars less than three times the larger amount. What’s the smaller amount? What is the largest amount?

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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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

Larger Amount

Four times the smaller amount is one hundred three dollars less than three times the larger amount.

Therefore:

Therefore:

Smaller Amount

Larger Amount

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step-by-step explanation: