Question

Sandy has $4,000 invested in stocks and bonds. Last year, she earned 8% interest

on the stocks and 6% interest on the bonds. At the end of the year, Sandy received
a check for $270. This was her annual income from the stocks and bonds. Which
system of equations below will determine s, the amount of money Sandy has
invested in stocks, and b, the amount invested in bonds?
F S + b = 4,000
Hs + b = 270
0.08s + 0.06b = 270
4,000
+ b = 270
S
Gs + b = 270
4,000 270 = s
Js + b = 4,000
0.06s + 0.08b = 270

Answer 1

To determine the amount of money Sandy has invested in stocks (s) and the amount invested in bonds (b), we can use the system of equations: Fs + b = 4,000, Hs + b = 2,700, and 0.08s + 0.06b = 270. Using the elimination method, we can solve for s and b. The solution is s = 65,000 and b = -61,000.

Step-by-step explanation:

The correct system of equations to determine the amount of money Sandy has invested in stocks, s, and the amount invested in bonds, b, is:

1. F s + b = 4,000
2. H s + b = 2,700
3. G 0.08s + 0.06b = 270

To solve the system, we can use the elimination method. First, we can eliminate b by subtracting Equation (2) from Equation (1). This gives us:

F - H s = 4,000 - 2,700

Simplifying, we get:

G -0.02s = 1,300

Dividing by -0.02, we find:

S s = -1,300 / -0.02

Solving for s, we get:

F s = 65,000

Next, substitute the value of s into Equation (1) to find b:

G 65,000 + b = 4,000

Rearranging, we get:

F b = 4,000 - 65,000

Simplifying, we find:

F b = -61,000

Therefore, the correct system of equations is: F s + b = 4,000, Hs + b = 2,700, and 0.08s + 0.06b = 270.