SOLUTION: Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 5.2% interest per year. He will put some of the money into Fund A that earns 2% per year and t

Algebra.Com
Question 1135537: Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 5.2% interest per year. He will put some of the money into Fund A that earns 2% per year and the rest in Fund B that earns 10% per year. How much should he invest into each fund (in dollars) if he wants to earn 5.2% interest per year on the total amount?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


With the traditional algebraic approach, you write and solve the equation that says x amount invested at 2%, plus ($55,000-x) invested at 10%, yields 5.2% on the total $55,000:



Straightforward algebra; but ugly numbers. I'll let you finish the solution by that method.

Here is a completely different method for solving this kind of "mixture" problem. It is based on the fact that the ratio in which the two need to be mixed is exactly determined by where the mixture percentage lies between the two given percentages.

Without any words of explanation, here are the required calculations:

10-5.2 = 4.8
5.2-2 = 3.2
4.8:3.2 = 3:2

The $55,000 must be split in two parts in the ratio 3:2 -- so $33,000 at one rate and $22,00 at the other.

Since 5.2% is closer to 2% than it is to 10%, the larger portion needs to be at 2%.

ANSWER: $33,000 at 2%; $22,000 t 10%
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The equation is


    0.02*a + 0.10*(55000-a) = 0.052*55000.


The solution is


    a =  = one click in Excel = 33000.


Answer.  $33000 to invest in fund A  and the rest $55000 - $33000 = $22000 to invest in fund B.


CHECK.   0.02*33000 + 0.10*22000 = 2860 dollars total interest = 0.052*55000.    ! Correct !


RELATED QUESTIONS

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him... (answered by ikleyn)
Translate to a system of equations and solve. Mark wants to invest $10,000 to pay for... (answered by Boreal)
Mark wants to invest $10,000 to pay for his daughter's wedding next year. He will invest... (answered by ikleyn)
Cara wants to invest $16,000 in certificates of deposit (CDs). For tax purposes, she... (answered by ikleyn)
Could you please help me with this problem? Mr.Cruz wants to borrow $40,000 from the... (answered by ikleyn,math_tutor2020)
Geoff has $5000 to invest. He wants to earn $568 in interest in one year. He will... (answered by ikdeep)
Geoff has $5000 to invest. He wants to earn $568 in interest in 1 year. He will invest... (answered by Theo)
Chris wants to put aside $2,000 to buy a house in the future. He decides to invest the... (answered by stanbon)
Hattie had $3850 to invest and wants to earn 2.9% interest per year. She will put some of (answered by richwmiller)