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Part 1
A total of $ 21,000$21,000 is to be​ invested, some in bonds and some in certificates of deposit​ (CDs). If the amount invested in bonds is to exceed that in CDs by $ 1,000 ,$1,000, how much will be invested in each type of​ investment? The amount invested in CDs is ​$

Answer 1

Let's define the variables:

- Let \( x \) be the amount invested in certificates of deposit (CDs).
- Let \( y \) be the amount invested in bonds.

According to the problem, we have the following two equations:

1. The total investment is $21,000:
\[
x + y = 21000
\]

2. The amount invested in bonds exceeds that in CDs by $1,000:
\[
y = x + 1000
\]

Now, we can substitute the second equation into the first equation to solve for \( x \):

\[
x + (x + 1000) = 21000
\]

Combining like terms:

\[
2x + 1000 = 21000
\]

Subtracting $1,000 from both sides gives:

\[
2x = 20000
\]

Now, divide by 2:

\[
x = 10000
\]

Now that we have \( x \), we can find \( y \):

\[
y = x + 1000 = 10000 + 1000 = 11000
\]

So, the amount invested in CDs is $10,000 and the amount invested in bonds is $11,000.

To summarize:

- Amount invested in CDs: **$10,000**
- Amount invested in bonds: **$11,000**