Rebecca H. answered • 01/16/17
Tutor
4.6
(5)
Algebra 2, Geometry, Trigonometry, and Precalculus
It helps to define variables first.
Let a = the amount of money in the 7% bond
Let b = the amount of money in the 11% bond
How does a relate to b?
If you aren't sure, create a few scenarios to help you answer the question.
If a = $3000, then what is b?
b would be $17000. What if a = $14000?
b would be $6000.
How does a relate to be?
b = 20000 - a
Ok, now that we have that established, how to we represent the interest from the 7% bond?
Remember the simple interest formula: I = Prt where I is interest, P is the amount invested, and t is time in years.
Ia = a (0.07) 1 because 7% as a decimal is 0.07 and the time is 1 year.
Ib = b (0.11) 1 because 11% as a decimal is 0.11 and the time is 1 year.
What else do you know about the interest collected? Well, the total interest is $1880, so Ia + Ib = 1880. Substitute the right sides of the equations for the interest to get:
0.07a + 0.11b = 1880
Bummer. We have two variables. But wait! b = 20000 - a! We can substitute and solve.
0.07a + 0.11(20000 - a) = 1880
Try solving this on your own, then scroll down to check.
0.07a + 0.11 (20000 - a) = 1880 Distribute.
0.07a - 0.11 a + 2200 = 1880 Subtract 2200 from both sides and combine the a terms.
-0.04a = -320 Divide by -0.04.
a = 8000
If a = $8,000, then b = $12,000. Remember to check:
Ia = 8000 (0.07) 1 = 560
Ib = 12000 (0.11) 1= 1320
Is Ia + Ib = 1880? --> 560 + 1320 = 1880? Yes! It checks.
