The sum of $305 was divided among 3 people so that the second received $4 less than twice as much as the first, and the third received $23 more than the second.
How much did the first person receive?
f s and t
s = 2f - 4
t = s + 23 = 2 f - 4 + 23 = 2 f + 19
f + s + t = f + 2f - 4 + 2 f + 19 = 305
5 f + 15 = 305
5 f = 290
f = 58
Let's assume the amount received by the first person is x dollars.
According to the given information:
- The second person received $4 less than twice as much as the first, which means the second person received (2x - $4) dollars.
- The third person received $23 more than the second person, which means the third person received ((2x - $4) + $23) dollars.
The total sum of $305 was divided among the three people, so we can write the equation:
x + (2x - $4) + ((2x - $4) + $23) = $305
Simplifying the equation:
x + 2x - $4 + 2x - $4 + $23 = $305
5x + $15 = $305
Subtracting $15 from both sides of the equation:
5x = $290
Dividing both sides of the equation by 5:
x = $58
Therefore, the first person received $58.
Let's assign variables to represent the amounts received by each person. Let's call the amount received by the first person "x" dollars.
According to the information given, the second person received $4 less than twice as much as the first person. This can be represented as: 2x - $4.
The third person received $23 more than the second person, which can be represented as: (2x - $4) + $23.
Now we can set up the equation based on the sum of the amounts received by all three people. The sum is $305:
x + (2x - $4) + ((2x - $4) + $23) = $305
To solve the equation, we can combine the similar terms:
x + 2x - $4 + 2x - $4 + $23 = $305
Combining like terms gives us:
5x +$15 = $305
Next, we can isolate the variable by subtracting $15 from both sides of the equation:
5x = $305 - $15
5x = $290
Finally, we can solve for x by dividing both sides of the equation by 5:
x = $290 / 5
x = $58
Therefore, the first person received $58.