A bank loaned out $17,000, part of it at the rate of 6% per year and the rest at 16% per year. If the interest received in one year totaled $2,000, how much was loaned at 6%?
This problem requires the utilization of basic algebra, a branch of mathematics focused on statements describing relationships between variables. Algebra dates back centuries, but is still quite relevant today, as it enables users to express variables and relationships into equations and solve for unknowns.
Answer and Explanation:
We are given the following two equations:
.06x + .16y = $2,000
x + y = $17,000
By embedding the second equation into the first, we can solve the problem. The computations and results are outlined below.
.06($17,000 - y) + .16y = $2,000
$1,020 - .06y + .16y = $2,000
.10y = $980
y = $9,800
We know y. Now, we can plug y into the second equation to solve x. See below.
x + $9,800 = $17,000
x = $7,200
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Learn more about this topic:
from SAT Subject Test Mathematics Level 2: Tutoring SolutionChapter 4 / Lesson 10