You have quarters and nickels saved in a piggy bank. there is a total of 3.45 in quarters and nickels and there are 9 more nickels than quarters. how many nickels and quarters in the piggy bank?

Total number of quarters=10

Total number of nickels=19

Step-by-step explanation:

The expression for the total value of money you have is;

Quarters have a value of= $0.25

Nickels have a value of= $0.05

Total value=(value of quarters×number of quarters)+(value of nickels×number of nickels)

where;

Total value=$3.45

Value of a quarter=$0.25

number of quarters=x

Value of a nickel=0.05

number of nickels=y, but y=x+9

replacing;

3.45=(0.25×x)+0.05(x+9)

3.45=0.25 x+0.05 x+0.45

3.45=0.3 x+0.45

0.3 x=3.45-0.45

0.3 x=3

x=3/0.3

x=10

y=x+9=10+9=19

Total number of quarters=10

Total number of nickels=19

4

step-by-step explanation:

(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