Suzy has a collection of quarters and dimes. Together she has 34 coins worth $6.40. How many quarters and how many dimes does Suzy have? Please show your work :)

Quarters = 20

Dimes = 14

Step-by-step explanation:

Dime = x = 10 cent = $0.1

Quarter = y = 25 cent = $0.25

x + y = 34 - - - (1)

0.1x + 0.25y = 6.40 - - - - (2)

From (1)

x = 34 - y

0.1(34 - y) + 0.25y = 6.40

3.4 - 0.1y + 0.25y = 6.40

3.4 + 0.15y = 6.40

0.15y = 6.40 - 3.40

0.15y = 3

y = 3 / 0.15

y = 20

x = 34 - y

x = 34 - 20

x = 14

Quarters = 20

Dimes = 14

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

step-by-step explanation:

4  

25

5258y

54.

t5

5r

54

5856

542

5458

86

.8558.65

565

565

55898

786

8/95

5896

8656265

556478