Genny babysits for two different families. One family paints her $6 an hour and a bonus of $20 at the end of the night. The other family pays her $3 every half hour and a bonus of $25 at the end of the night. Write and solve the system of equations that represent this situation. At what number of hours do the two families pay the same for the babysitting services from Genny?

Question

Genny babysits for two different families. One family paints her $6 an hour and a bonus of $20 at the end of the night. The other family pays her $3 every half hour and a bonus of $25 at the end of the night. Write and solve the system of equations that represent this situation. At what number of hours do the two families pay the same for the babysitting services from Genny?

Answer 1

The two families pay the same per hour. $6 an hour is the same as $3 for half an hour. The only difference is the bonus.

It doesn't make any difference how many hours each work.

Answer 2

6x-20=y

3x-25=y

Answer 3

Let's assume the number of hours that Genny babysits for is represented by "x".

For the first family:
They pay Genny $6 per hour, so the payment for the first family would be: 6x
They also give her a bonus of $20 at the end of the night

For the second family:
They pay Genny $3 every half hour, so the payment for the second family would be: 3(2x) = 6x
They also give her a bonus of $25 at the end of the night

So, the two equations that represent the total payment for Genny in two different families are:
1) Payment for the first family = 6x + 20
2) Payment for the second family = 6x + 25

To find the number of hours at which the two families pay the same, we set the two equations equal to each other and solve for x:
6x + 20 = 6x + 25

By subtracting 6x from both sides, we have:
20 = 25

This is not a true statement. Therefore, there is no number of hours at which the two families pay the same for the babysitting services from Genny.

Answer 4

To write a system of equations that represent this situation, let's denote the number of hours Genny babysits by 'h'.

For the first family:
They pay her $6 per hour, so the amount they pay her for h hours of babysitting is 6h.
They also give her a bonus of $20, so the total amount they pay her is 6h + 20.

For the second family:
They pay her $3 every half hour, so for h hours of babysitting, they pay her 2 * 3h = 6h.
They also give her a bonus of $25, so the total amount they pay her is 6h + 25.

Thus, we have the following system of equations:

Equation 1: 6h + 20 = 6h + 25

To solve this equation, we can start by simplifying it:

Equation 1: 20 = 25

This equation does not have a solution. The two families never pay the same amount for the babysitting services, regardless of the number of hours Genny works.