Question

find the number of full 8 hour shifts that jenna worked last month. she worked twice as many 6 hour shifts as 8 hour shifts she worked a total of 280 hour last month

Answer 1

are we assuming that there are only 8 hour and 6 hour shifts?

Answer 2

I guess yes

Answer 3

Have you learned systems of equations?

Answer 4

No

Answer 5

Ok.
Since we don't know the number of 6-hour or 8-hour shifts, we need a variable to represent the number of 8-hour shifts.
Let's call x the number of 8-hourt shifts.

Answer 6

If she worked twice as many 6-hour shifts as 8-hour shifts, and she worked x 8-hour shifts, then using x, how many 6-hour shifts did she work?

Answer 7

2

Answer 8

Close. Not just 2, but 2 times x or 2x.

Answer 9

Ok?

Answer 10

Yup

Answer 11

Ok. We need one more step. then we can write an equation.

In an 8-hour shift, she works 8 hours. This is obvious.
In 2 8-hour shifts, she works 2 * 8 hours = 16 hours.
In 3 8-hour shifts, she works 3 * 8 hours = 24 hours.
In x 8-hour shifts, she works how many hours?

Answer 12

8x or 8 hours

Answer 13

No. You got it right the first time. In x 8-hour shifts, she works x * 8 hours, or 8x hours.

Answer 14

Ok so 8 times x is 8x

Answer 15

Now we can put all the information together and write an equation.

Answer 16

Correct.

Answer 17

She worked x 8-hour shifts. That means she worked 8x hours in 8-hour shifts.
She worked 2x 6-hour shifts. That means she worked 2x * 6 = 12x hours in 6-hour shifts.
She worked a total of 280 hours.

That means that

8x + 12x = 280

Answer 18

Now we solve that equation to find x, the number of 8-hour shifts she worked.

Answer 19

Since 8x and 12x are like terms, you can add them together.

Answer 20

to get 20x

Answer 21

Correct.
Now we have

20x = 280

We divide both sides by 20 to find x.

Answer 22

and you get 14 which would represent 14, 8 hour shifts

Answer 23

Correct.

Answer 24

Now let's see if the answer makes sense.

Answer 25

Remember she worked twice as many 6-hour shifts as she worked 8-hour shifts.
That means she worked 14 8-hour shifts and 28 6-hour shifts, right?

Answer 26

how did you get 28 6 hour shifts

Answer 27

nevermind i see 14 times 2

Answer 28

Good.

Answer 29

because its twice the time

Answer 30

Now let's see if the total number of hours really adds up to 280.

14 * 8 = 112
28 * 6 = 168
112 + 168 = 280

Yes, the number of hours adds up to 280, so our answer is correct.

Answer 31

Ok, gtg. Bye.

Answer 32

ok thanks i first thought that since twice 6 hour shifts then its 12 just divided by 280 but you have to include the 8 to

Answer 33

Correct. You need to account for both the 6-hour and 8-hour shifts.

Answer 34

yup ok