Question

Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.

Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.

Answer 1

Divide 1,470/5 =294 so its possible it could be any whole number if equal amounts sold.

Divide 1470/4 = 3.57.5 so it could be possible when even sandwiches are sold there would be half = .5 result.

Divide 1450/6 = 241.666 so it could be possible when even amounts of wraps are sold there would be 2/3 result .666

Either of these could add to .666 + -5 = (+1).166

or when wraps are odd amounts ie) 2+9 = 11 1470/11 = (133).6363

So we now know the amounts have to be even amounts sold.

2x +3y = 1,470

xy =1,470/5

xy = 294 = 1

1 x 294/5 = xy/1

=(x1)58 8/10= xy/1

(x= )2 x 58 8/10 = 117 6/10

(y =) 3 x 58 8/10 = 176 4/10

x=$117.60

y=$176.40

Explanation:

You need to map a graph and label total profit wraps at the bottom x line

Count units in 20's 2x5 lines each 10 units to show 0-20-40-60...all the way up to 180. So you can dot at 176.4

For the y axis you need to show 0,20,40,60...all the way up to 120 and label y axis sandwiches 176.4 as this is the shorter line and it will save graph paper.

Then cross each point coordinate at 117.6 at 117 as close above this possible between 100-120 so y axis for sandwich shows $2 on y axis and x shows x= 117.6 y=2 and then all you need to do is color code wraps axis x = 3 y=176.4

Remember if you do this way it is correct the only difference is that idea 2+ 3 is close range number is shown idea 1 doesn't separate them completely in labeling so the equation shows 2 and 3 always and shows this combined shows the price set, the profit and if you want to make the graph in decimals 10-20-30-40 it would take up too much graph paper so go up in 20's and estimate your answer wraps 176.4 for example 3/4 between 160-180

2. Suppose Sal's total profit on lunch specials for the next month is $1,593

When profit is shown as the same you would have to split this in half and show Sally Total profit 1,593/2 = 750+46.5 = 796.50 for each sandwich and wrap so this graph goes up in 50's.

Then when that is finished both graphs side by side on two pages in the book we compare them write how the 2 months are similar because they both have the close range functions for x and y, where pence is shown in a unique way as the amounts are shown in $ values and we can read to the nearest dollar just about. While the cent value can be read through the equation fractions if needed upon the same points of profit. whilst cost is not labeled on both opposite axis we can stick to the rule in each that profit is upon the function and shown on each line opposite. We know its cost upon the same cross of opposite function just so we can separate both values cent and dollar while profits of sandwich and wrap are also both separated.

hope this can help you understand separating sandwiches from wraps is the better options for both graphs and is exactly what is asked of.