Unformatted text preview: EXAMPLE 6 Solving a Joint Variation Problem
The interest on a loan or an investment is given by the formula I = prt. Here, for a
given principal p, the interest earned, I, varies jointly as the interest rate r and the
time / the principal is left earning interest. If an investment earns $100 interest at 5%
for 2 yr, how much interest will the same principal earn at 4.5% for 3 yr?
We use the formula I = prt, where p is the constant of variation because it is the
same for both investments.
I = prt
Here, p is the constant of variation.
Solve for p.
100 = p(0.05) (2)
Let / = 100, r = 0.05, and t = 2.
100 = 0.1p
p = 1000
Divide by 0.1. Rewrite.
Now we find / when p = 1000, r = 0.045, and t = 3.
1 = 1000(0.045) (3) = 135 Let p = 1000, r = 0.045, and t = 3.
The interest will be $135.
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- Spring '19
- 5%, $100, 4.5%, $135