Betsy, a recent retiree, requires $6,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 13% per year or in a certificate of deposit (CD) paying 3% per year. How much money should be invested in each to realize exactly $6,000 in interest per year?

$45,000 at 13% =  B-rated bond

$5,000 at 3% = CD

Step-by-step explanation:

Let us assume the x amount at 13% be 0.13x

And, y amount at 3% be 0.03x

Total interest = $6,000

The equation is

0.13x + 0.03x = $6,000 (1)

Now the total amount is $50,000

So

x + y = $50,000

y = $50,000 - x (2)

Now put the y value in the equation 1

So,

0.13x + 0.03 ($50,000 - x)  = $6,000

0.13x + $1,500 - 0.03x = $6,000

0.10x = $6,000 - $1,500

0.10x = $4,500

x = $4,500 ÷ 0.10

= $45,000 at 13%

now y value would be

= $50,000 - $45,000

= $5,000 at 3%

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

answer: group b.

step-by-step explanation: