Answers:
Note: the commas are to help the large numbers look more readable. The computer system may not accept commas when you input the answers, so be sure to double check.
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Work Shown:
x = amount invested in stocks
y = amount invested in bonds
z = amount invested in savings account
x+y+z = 300,000 since this is the total amount he invests among the three types of accounts. Call this equation (1).
He invested four times as much in stocks compared to the savings account, so x = 4z. Call this equation (2).
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x = amount invested in stocks
0.15x = amount of money earned from the stocks (15% return)
y = amount invested in bonds
0.10y = amount of money earned from the bonds (10% return)
z = amount invested in bonds
0.04z = amount of money earned from the savings account (4% return)
0.15x+0.10y+0.04z = total return from the three accounts combined
0.15x+0.10y+0.04z = 35,600
Call this equation (3).
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We have these three equations
Start with equation (1). Replace every x with 4z. This is valid because equation (2) states that x = 4z. Therefore every x is the same as 4z. After the replacement is done, simplify and solve for y
x+y+z = 300,000
4z+y+z = 300,000
y+5z = 300,000
y= -5z+300,000
Call this equation (4).
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Move to equation (3). We will plug in x = 4z and y= -5z+300,000. Doing these two moves will turn equation (3) into an equation with z as the only variable.
Solve for z.
0.15x+0.10y+0.04z = 35,600
0.15(x)+0.10(y)+0.04z = 35,600
0.15(4z)+0.10(y)+0.04z = 35,600 ... plug in equation (2)
0.15(4z)+0.10(-5z+300,000)+0.04z = 35,600 ... plug in equation (4)
0.60z-0.50z+30,000+0.04z = 35,600 ... distribute
0.14z+30,000 = 35,600
0.14z = 35,600 - 30,000 ... subtract 30,000 from both sides
0.14z = 5,600
z = 5,600/0.14 .... divide both sides by 0.14
z = 40,000
Use this to find the value of x
x = 4*z
x = 4*40,000
x = 160,000
Also, use this z value to find the value of y
y = -5z+300,000
y = -5(40,000)+300,000
y = -200,000+300,000
y = 100,000
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So,
x = 160,000
y = 100,000
z = 40,000
meaning that,
