MATH SOLVE

4 months ago

Q:
# Could anybody give me some help? I'm a little confused .-. <3 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 from last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold. ( Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences)

Accepted Solution

A:

What your teacher wants is for you to isolate y in the given equation. In other words, get y all by itself.

To do this, you'll do two basic steps:

Step 1) Subtract 2x from both sides

Step 2) Divide both sides by 3

Let's do that and we get...

2x+3y = 1470

2x+3y-2x = 1470-2x ... apply step 1

3y = 1470-2x

3y = -2x+1470

3y/3 = (-2x+1470)/3 ... apply step 2

y = (-2x)/3 + 1470/3

y = (-2/3)x + 490

After isolating y, we get y = (-2/3)x + 490

To get this into function notation, we simply replace y with f(x) to get the final answer f(x) = (-2/3)x+490 which is the same as writing [tex]f(x) = -\frac{2}{3}x+490[/tex]

This graph represents all of the ordered pairs (x,y) that make the original equation true. For example, the point (x,y) = (0,490) is on the line where x = 0 and y = 490. This point is when 0 sandwiches are sold and 490 wraps are sold yielding a profit of $1470. Another point on this line is (x,y) = (3,488). Now 3 sandwiches have been sold along with 488 wraps leading to the same profit of $1470. Any ordered pair point you pick on the line should lead you to the same profit.

To do this, you'll do two basic steps:

Step 1) Subtract 2x from both sides

Step 2) Divide both sides by 3

Let's do that and we get...

2x+3y = 1470

2x+3y-2x = 1470-2x ... apply step 1

3y = 1470-2x

3y = -2x+1470

3y/3 = (-2x+1470)/3 ... apply step 2

y = (-2x)/3 + 1470/3

y = (-2/3)x + 490

After isolating y, we get y = (-2/3)x + 490

To get this into function notation, we simply replace y with f(x) to get the final answer f(x) = (-2/3)x+490 which is the same as writing [tex]f(x) = -\frac{2}{3}x+490[/tex]

This graph represents all of the ordered pairs (x,y) that make the original equation true. For example, the point (x,y) = (0,490) is on the line where x = 0 and y = 490. This point is when 0 sandwiches are sold and 490 wraps are sold yielding a profit of $1470. Another point on this line is (x,y) = (3,488). Now 3 sandwiches have been sold along with 488 wraps leading to the same profit of $1470. Any ordered pair point you pick on the line should lead you to the same profit.