. Vern sold his 1964 Ford Mustang for $55,000 and
wants to invest the money to earn him 5.8% interest
per year. He will put some of the money into Fund A
that earns 3% per year and the rest in Fund B that
earns 10% per year. How much should he invest into
each fund if he wants to earn 5.8% interest per year on
the total amount?
So I have the answer for this but I not sure on the method.
I believe you are suppose to set it up like I=PRT but with there being two equation. I get lost
amount invested at 10% interest ---- x
amount invested at 3% interest ---- y
x + y = 55000 ----> y = 55000-x
.10x + .03y = .058(55000)
multiply each term by 100
10x +3y = 5.8(55000) = 319000
now use substitution:
10x + 3(55000-x) = 319000
tidy it up ....
whoa where u get 319000 from?
it shouldve been 3190.
this is what I have....
A=55000-B
55000(.058)(1)
.03A+(55000-B)(.1)
3190=.03B+5500-.1B
.....It should come out to 33000 for B and A is 22000.
I appreciate the help because it gives me some kind of guidance of where to begin at
I skipped the obvious step from
.10x + .03y = .058(55000)
to
.10x + .03y = 3190
now multiply each term by 100
10x + 3y = 319000
why would u multiple by 100 if you have 3190. that part you lost me. I made a mistake earlier .03a should be .03b+(55000-B)
To solve this problem, you can set up a system of equations using the information given:
Let's assume Vern invests x dollars in Fund A and the remaining (55000 - x) dollars in Fund B.
Fund A earns 3% interest, so the interest earned from Fund A would be (x * 0.03).
Fund B earns 10% interest, so the interest earned from Fund B would be ((55000 - x) * 0.10).
Vern wants to earn a total of 5.8% interest from the total amount, so the interest earned from the entire investment would be:
Total Interest = (x * 0.03) + ((55000 - x) * 0.10)
Since the interest earned should be equal to 5.8% of the total amount:
Total Interest = 0.058 * 55000
Now you can set up the equation by equating the two expressions for Total Interest:
(x * 0.03) + ((55000 - x) * 0.10) = 0.058 * 55000
Simplifying the equation:
0.03x + 0.10(55000 - x) = 0.058 * 55000
0.03x + 5500 - 0.10x = 3190
-0.07x + 5500 = 3190
-0.07x = 3190 - 5500
-0.07x = -2310
Dividing both sides of the equation by -0.07 to solve for x:
x = (-2310) / (-0.07)
x ≈ 33000
Therefore, Vern should invest approximately $33,000 in Fund A and the remaining (55000 - 33000) = $22,000 in Fund B in order to earn 5.8% interest per year on the total amount.