Answer:
$8,500 in CDs; $11,500 in bonds
Step-by-step explanation:
Let c = amount invested in CDs.
Let b = amount invested in bonds.
"A total of $20,000 is to be invested, some in bonds and some in certificates of deposit (CDs)."
From the total investment, we get this equation.
c + b = 20000
"If the amount invested in bonds is to exceed that in CDs by $3000"
From the details of the amounts, we get this equation.
b = c + 3000
We have a system of equations in two unknowns.
c + b = 20000 Eq. 1
b = c + 3000 Eq. 2
Since Eq. 2 is already solved for b, we will use the substitution method to solve the system of equations.
Substitute b in Eq. 1 with c + 3000.
c + c + 3000 = 20000
2c + 3000 = 20000
2c = 17000
c = 8500
Now substitute c = 8500 in Eq. 2 and solve for b.
b = c + 3000
b = 8500 + 3000
b = 11500
Answer: $8,500 in CDs; $11,500 in bonds
