You invested $6000 in two accounts paying 7% and 9% annual interest. at the end of the year, the total interest from these investments was $510. how much was invested at each rate?

The amount invested at 7% was $1,500 and the amount invested at 9% was $4,500

Step-by-step explanation:

we know that

The simple interest formula is equal to

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem

Let

x-----> the amount invested at account paying 7%

(6,000-x) -----> the amount invested at account paying 9%

substitute in the formula above

Solve for x

therefore

The amount invested at 7% was $1,500 and the amount invested at 9% was $4,500

y=mx+b

step-by-step explanation:

m slope

b y-intercept

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