Abank wishes to invest a $100, 000 trust fund in three sources: bonds paying 8%; certificates of deposit paying 7%; and first mortgages paying 10%. the bank wishes to realize an $8, 000, annual income from the investment. a condition of the trust is that the total amount invested in bonds and certificates of deposit must be triple the amount invested in mortgages. how much should the bank invest in each possible category?

It is not possible to make the investment under the given conditions.

Step-by-step explanation:

Let x, y and z be the amounts invested in bonds, certificates of deposit and mortgages respectively.

1st equation

“A bank wishes to invest a $100, 000 trust fund in three sources”

x + y + z = 100,000

2nd equation

“The bank wishes to realize an $8, 000, annual income from the investment and bonds paying 8%; certificates of deposit paying 7%; and first mortgages paying 10%”

0.8x + 0.7y + 0.1z = 8,000

3rd equation

“the total amount invested in bonds and certificates of deposit must be triple the amount invested in mortgages”

x+y = 3z

and we have a linear system of 3 equations with 3 unknowns

    x +      y +      z = 100,000

0.8x + 0.7y + 0.1z = 8,000

    x +      y      -3z = 0

This system has a unique solution given by

x = -470,000  

y = 545,000

z = 25,000

Since x is negative, we deduct there is no way to do such an investment.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

(-5,-28)

i graphed to on desmos.