Donica wants to join a gym.
Gym A: $20 joining fee and $40 monthly charge.
Gym B: No joining fee and $45 monthly charge.
Enter the number of months it will take for the total cost for both gyms to be equal.

It will take four months.

Step-by-step explanation:

We can easily solve this by using an equation. Lets substitute y for the amount of months and b for the joining fee. M will be the monthly charge.

Our equation is my+b=my+b

Substitute the known values.

(40)y+20=(45)y+0. The joining fee for gym b is zero because it has no joining fee. All we need to do now is solve.

Subtract 40y on both sides to combine like terms.

20=5y

Now divide by 5 to isolate y.

4=y

It will take four months for the cost of both gyms to be equal. Just to check, lets substitute 4 for y.

40(4)+20=45y

Multiply.

160+20=180

Add.

180=180.

Hope this helps!

4

Step-by-step explanation:

x=# months

20+40x=45x

     -40x  -40x

––––––––––

 20= 5x

÷5    ÷5

4 = x  or

x=4    

n

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