Ashley has some pennies and some nickels. she has at most 22 coins worth a minimum of $0.78 combined. if ashley has 4 pennies, determine the minimum number of nickels that she could have. if there are no possible solutions, submit an empty answer.

The minimum number of nickels that she could have is 15

Step-by-step explanation:

Let x represent the number of nickels Ashley has. If she has 4 pennies and has at most 22 coins, then

→ x + 4 <= 22

→ x <= 18    (1)

Her coins worth a minimum $0.78. Also, it is known that 1 dollar is equal to 100 cents and 1 nickel is equal to 5 cents.

→ (x * 5) + 4 >= 78

→ 5x >= 74

→ x >= 14.8  (2)

If we combine the equation 1 and 2:

14.8 <= x <= 18

The minimum value of x is 15

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

(-5,-28)

i graphed to on desmos.