SOLUTION: Need help solving other problems. I never know where to start with forming an equation. 1. Investing 30,000, part at 5% and the rest at 10%. What is the most I can invest at 5

Question 317353: Need help solving other problems. I never know where to start with forming an equation.
1. Investing 30,000, part at 5% and the rest at 10%. What is the most I can invest
at 5% and still be guaranteed at least $2000 in interest per year?
2. If I can be paid for my skills in one of two ways, with 2 different plans.
Plan A: pays $300 plus $9.00 per hour.
Plan B: Straight $12.50 per hour
Now suppose that the job takes n hours. For what value of n is plan b better for me.
Please just explain how to figure out the equations, I would like to solve the equation myself if possible.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Investing 30,000, part at 5% and the rest at 10%. What is the most I can invest at 5% and still be guaranteed at least $2000 in interest per year?
---
Using two variable and two equations you get:
---
Quantity Equation: x + y = 30,000 dollars
Interest Equation: 0.05x + 0.10y = 2000 dollars
---
Multiply thru the 1st equation by 10.
Multiply thru the 2nd equation by 100:
Quant: 10x + 10y = 300000
Inter: 5x + 10y = 200000
-----
Subtract the 2nd from the 1st and solve for "x":
5x = 100,000
x = $20,0000 (amt. to be invested at 5%
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2. If I can be paid for my skills in one of two ways, with 2 different plans.
Plan A: pays $300 plus $9.00 per hour.
Equation A: A(n) = 300 + 900n
------------------------------------
Plan B: Straight $12.50 per hour
Equation B: B(n) = 12.50n
-------------------------------------
Now suppose that the job takes n hours. For what value of n is plan b better for me.
---
Solve for "n":
12.50n > 300 + 9n
---
3.5n > 300
n > 85.71
Round up to get:
n >= 86 hours.
======================
Cheers,
Stan H.
==================

Please just explain how to figure out the equations
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