To purchase a car costing $10,000, the buyer bor- rowed part of the money from the bank at 9% sim-
ple interest and the rest from her mother-in-law at
12% simple interest. If her total interest for the year
was $1080, how much did she borrow from the
bank?

She borrowed 4000 from bank.

Step-by-step explanation:

Let 'y' be the amount borrowed from bank. Then 10000-y is the amount borrowed from her mother-in-law.

Let x= interest amount gained by bank . Then 1080- x = interest gained by mother-in-law

I1= interest rate by bank= 9%

I2= interest rate by mother-in-law=12%

Time(T) = 1 year

Now, By Simple Interest formula:

x=PTR/100

Or, x=(y*1*9)/100

Or,100x=9y

or,9y-100x=0Equation (i)

Again 1080-x= ((10000-y)*1*12)/100

Or, 108000-100x=120000-12y

Or, 12y-100x=12000Equation(ii)

Solving equation (i) and (ii), we get

y= 4000, which the amount borrowed from bank.

3x3 = 9 and 2x2 = 4

step-by-step explanation:

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