Asandwich store charges a delivery fee to bring lunch to an office building. one office pays $33 for 4 turkey sandwiches. another office pays $61 for 8 turkey sandwiches. how much does each turkey sandwich add to the cost of the delivery? explain how you know.

Step-by-step explanation:

Let each turkey sandwich cost x, and the fixed delivery fee be y.

From the first situation, 4x + y = 33

From the second case with 8 sandwiches, 8x + y = 61

Subtracting the first equation from the second gives 4x = 28

x = 7

Substituting this back into the first equation gives y = 5.

Therefore, each turkey sandwich costs $7 and the delivery fee is $5.

If you were to have 12 turkey sandwiches delivered, the cost would be 12x + y = 12*7 + 5 = $89, so this would be more than $85.

If you want to do it graphically, convert both equations into slope-intercept form.

y = -4x + 33 and y = -8x + 61

For the first equation, the y-intercept is (0,33) and the x-intercept is (33/4, 0).

For the second equation, the y-intercept is (0,61) and the x-intercept is (61/8, 0).

Connect the intercepts for each equation, then find the point of intersection. The x- and y-coordinates of the point of intersection are x = 7 and y = 5, which are the values that will solve the equations.

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step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.