four people invested in a restaurant. one person invested $1000,000. two others invested in the ratio x:2x, and the fourth person invested an amount equal to the other three investors combined. the total investment was $1,100,000. A. write an expression for the amount invested by the fourth person. B. write an equation that allows you to find the amount invested by each person. C. How much did each person invest?
If the 4th person invested y, then
1,000,000 + x + 2x + y = 1,100,000
But y is as much as the other three together, so
y+y = 1,100,000
y = 550,000
I'm sure you can now find the other answers.
B. 100,000+x+2x+550,000=1,100,000
3x=1,100,000-650,000
3x=450,000
x=450,000/3
x=150,000
c. 1. 100,000
2. 150,000
3. 300,000
4. 550,000
A. Let's assume the amount invested by the fourth person is "y" dollars.
B. To find the amount invested by each person, we can set up an equation based on the given information. The equation is:
$1,000,000 + x + 2x + y = $1,100,000
C. Now, let's solve the equation:
Combining like terms, we have:
$3,000,000 + 3x + y = $1,100,000
Subtracting $1,100,000 from both sides, we get:
3x + y = $100,000
Since the fourth person invested an amount equal to the other three investors combined, we can rewrite the equation as:
3x + y = 3x + 2x
This simplifies to:
y = 2x
Now, substitute this expression for "y" in the earlier equation:
2x = $100,000
Divide both sides by 2:
x = $50,000
Now, substitute this value of "x" back into the equation to find the amount invested by the fourth person:
y = 2($50,000)
y = $100,000
So, each person invested the following amounts:
First person: $1,000,000
Second person: $50,000
Third person: $100,000
Fourth person: $100,000
A. To write an expression for the amount invested by the fourth person, let's assume the ratio of the second and third person's investment as x:2x, where x is a variable representing the amount invested by the second person.
Using this, the fourth person's investment can be represented as the sum of the other three investors' investments combined, which is $1000,000 + x + 2x.
B. To write an equation that allows us to find the amount invested by each person, we can set up an equation using the given information. The total investment of all four people is $1,100,000:
$1000,000 + x + 2x + ($1000,000 + x + 2x) = $1,100,000
Simplifying this equation, we get:
$1000,000 + 5x = $1,100,000
C. Now, we can solve the equation to find the value of x, and subsequently the investments made by all four people.
$1000,000 + 5x = $1,100,000
Subtracting $1,000,000 from both sides:
5x = $100,000
Dividing both sides by 5:
x = $20,000
Using this value of x, we can calculate the investments made by each person:
The first person invested $1,000,000.
The second person invested $20,000.
The third person invested 2x = 2 * $20,000 = $40,000.
The fourth person invested the sum of the other three investors' investments, which is $1,000,000 + $20,000 + $40,000 = $1,060,000.