Set Up Correct Equations...2

mathdad

mathdad

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Do not solve. Set up the correct equations.

A person has 20,000 dollars to invest. As the person’s financial consultant, you recommend that the money be invested in Treasury bills that yield 4 percent, Treasury bonds that yield 8 percent, and corporate bonds that yield 12 percent. The person wants to have an annual income of 1560 dollars, and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment.

My Work:

Let x = treasury bills

Let y = treasury bonds

Let z = corporate bonds

0.40x + 0.04y + 0.12z = 20,000
x + y + z = 1560
z = (1/2)x

Correct?
 
Equations 1 and 2 are wrong if equation 3 is correct. I cannot imagine under what definitions equation 1 would be correct under any definition of the variables relevant to this problem. Let's try more descriptive names.

x= amount invested in T bills
y = amount invested in T bonds
z = amount invested in C bonds

Do you see that your names do not tell you whether your variables stand for income derived or amount invested. Your third equation makes sense only if x and z represent amounts invested as I have defined them above.

Those definitions allow us to translate English directly into math with your equation 3, namely

[MATH]z = \frac{1}{2} * x[/MATH]
and those definitions also lead very obviously to [MATH]x + y + z = 20000.[/MATH]
Now what is the third equation using those definitions of the variables?

Note that the naming step is not purely mechanical; the names chosen must be informative enough to help us think through how they apply to the problem.
 
JeffM said:
Equations 1 and 2 are wrong if equation 3 is correct. I cannot imagine under what definitions equation 1 would be correct under any definition of the variables relevant to this problem. Let's try more descriptive names.

x= amount invested in T bills
y = amount invested in T bonds
z = amount invested in C bonds

Do you see that your names do not tell you whether your variables stand for income derived or amount invested. Your third equation makes sense only if x and z represent amounts invested as I have defined them above.

Those definitions allow us to translate English directly into math with your equation 3, namely

[MATH]z = \frac{1}{2} * x[/MATH]
and those definitions also lead very obviously to [MATH]x + y + z = 20000.[/MATH]
Now what is the third equation using those definitions of the variables?

Note that the naming step is not purely mechanical; the names chosen must be informative enough to help us think through how they apply to the problem.
Click to expand...

The third equation is x + y + z = 1560. I can replace z with (x/2). So, I get x + y + (x/2) = 1560.
 
mathdad said:
Do not solve. Set up the correct equations.

A person has 20,000 dollars to invest. As the person’s financial consultant, you recommend that the money be invested in Treasury bills that yield 4 percent, Treasury bonds that yield 8 percent, and corporate bonds that yield 12 percent. The person wants to have an annual income of 1560 dollars, and the amount invested in corporate bonds must be half that invested in Treasury bills. Find the amount in each investment.

My Work:

Let x = treasury bills

Let y = treasury bonds

Let z = corporate bonds

0.40x + 0.04y + 0.12z = 20,000
x + y + z = 1560
z = (1/2)x

Correct?
Click to expand...
First you have to redefine x, y & z as suggested in response # 2.
 
mathdad said:
x= amount invested in T bills
y = amount invested in T bonds
z = amount invested in C bonds
Click to expand...
"...A person has 20,000 dollars to invest"

Now as for the next equation - do you see -

x + y + z < = 20000
 
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