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Temka [501]
3 years ago
8

Plz help (This is the whole problem it says "one part remaining")

Mathematics
2 answers:
stiks02 [169]3 years ago
8 0
Hey there!

To start, let x represent the cost of the mutual fund that earned 9%.

This cost will be represented by the term 0.09x.

Now, let (1200-x) represent the cost of the mutual fund that earned 3% profit, since the two amounts must add up to be 1200, the amount the investor originally invested. 

This cost will be represented by 0.03(1200-x)

Next, because the overall profit of the two mutual funds earned was 78 dollars, you can set up this equation:
0.09x+0.03(1200-x)=78

Now, solve for the value of x:
0.09x+0.03(1200-x)=78
0.09x+36-0.03x=78
0.06x+36=78
0.06x=42
x=700

Therefore, the amount invested in the 9% mutual fund would be $700 dollars.

Hope this helps and have a wonderful day! :)
Shalnov [3]3 years ago
3 0
He invested two unknown amount that add to $1200.
Let the amount invested at 9% be x.
Let the amount invested at 3% be y.

The amounts add to $1200.
x + y = 1200           First Equation

The profit from the 9% part is 0.09x.
The profit from the 3% part is 0.03y.
The two profits add to $78.
0.09x + 0.03y = 78        Second Equation

We have two equations in two unknowns, so we can solve this problem as a system of equations.

x + y = 1200
0.09x + 0.03y = 78

Multiply the first equation by -0.09 and add to the second equation.

-0.09x - 0.09y = -108
 0.09x + 0.03y =   78
----------------------------
             -0.06y = -30

Divide both sides by -0.06

y = 500

Now we substitute 500 into y in the first equation.

x + y = 1200

x + 500 = 1200

x = 700

Answer: The amount invested at 9% is $700
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3 years ago
Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions
Bingel [31]

These are three equations and three answers.


Answers:

  • A) infinite solutions, identity
  • B) one solution, x = 27, neither contradiction nor identiy
  • C) x = no solutions, contradiction

Explanation:


Equation A: 20 - 4x = 12 - x + 8 - 3x

The objective is clearing the unknown, which is to isolate it in one side of the equation.

These are the steps and properties that you need to use:


1.  Combine like terms on right side:

20 - 4x  = 20 - 4x


2. Use addition property of equality (add 4x on each side).

20 = 20 ↔ identity


Conclusion: you have gotten a condition that is always true, no matter the value of x, which means that the equation has infinite solutions and it is an identity.


Equation B: 5x + 4x - 3  =  24 + 8x (note that I placed the equal sign as it was missing)


1.  Combine like terms on each side:

9x - 3 = 24 + 8x


2. Subtraction property and addition propertiy of equality (subtract 8x and add + 3 on both sides)

x = 27 ↔ solution (neither contradiction nor identity)


Conclusion: the solution is x = 27.


Equation C: 5x + 6 = 2x + 6 + 3x - 15 (note that I placed the equal signs as it was missing)


1. Comitne like terms on the right side:

5x + 6 = 5x - 9


2. Subtraction property of equality (subtract 5x from each side)


6 = - 9 ↔ contradiction


Conclusion: the equation does not have a solution since the final equality is always false (a condradiction or absurd).


For your information, when the variable (x) dissapears and fhe final equality is always true (for example 0 = 0, or 20 = 20), the equation is an identity.

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3 years ago
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Steven and James are both about to take a math test. Steven is experiencing shortness of breath and profuse sweating in anticipa
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Answer:

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Step-by-step explanation:

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3 years ago
suppose for everyone cup of rice I add 2 3/4 cups of water. If I add 2 1/2 cups of rice, how much cups of water do I add?
Brrunno [24]

Answer:

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Step-by-step explanation:

Since 1 cup of rice is added to 2 3/4 water

We are to determine the Amount of water to be to 2 1/2 cups of rice

Let the unknown number for water be x

So let's solve

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Cross multiply

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Step-by-step explanation:

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