Direct Variations

[MichelleHib]

Need help with writing a direct variation problem.

If one thing increases and that causes the other to also increase, we say the two concepts Vary Directly. If an incease in the first causes a decrease in the second, we say the two concepts vary inversely.


Write a complete solution to the variation problem, showing all steps used in solving the problem and post it to the discussion board. Explain each step as if you were the expert explaining it to a novice.

For a given interest rate, simple interest varies jointly as principal and time. If $5000 is left in an account for 8 years earns interest of $1600, how much interest would be earned if you deposit $10000 for 7 years?

(Figuring this out in my head I know that the interest rate is .04% but I can't figure out how to write it as a variation problem.)
5000 x .04%(given interest rate) for 8 years = $1600
10000 x 04%(% for 7 = $2800

y=kx (This is how the formula is supposed to start--I guess?)
y=1600
k= 40000 (5000 x 8)
x= .04
(Am I plugging in the numbers right here?)


y=1600, x=5000 x 8

1600=k(5000) x 8
/ /
5000 5000 x 8
16 = 40,000
50
8 = 40,000
25

(25) 8 = 40000 (25)
25
8 = k1600
1600 1600

.005 = k??????

 

[MichelleHib]

Direct Variance

Thank you figment!

 

[lookagain]

8(5000r) = 1600 : solve to get r = .04

7(10000r) = x
x = 10(10000(.04)) = 2800\(\displaystyle \ \ \ \ \)<------- Typo.

x = 7(10000(.04))