A sandwich shop is ordering apples and grapes to make chicken salad. Apples cost $2.19 per pound and grapes cost $2.60 per pound. If they ordered a total of 20 pounds of apples and grapes and paid $35.80, how many pounds of grapes did they order? We got $19.51 but we think it is wrong.

Less than 13 pounds of grapes,

as 14 pounds of grape exceeds $35.80,

If you order as low as zero pounds of grapes, then the price of apple pounds would be $35.80/20 =$1.79 per pound

Step-by-step explanation:

Let

Quantity of Apple and grapes=20

Cost of apple=$2.19

Cost of grape=$2.60

Total cost of apple and grape=$35.80

a+g=20

a=20-g

PaQa+PgQg=35.80

2.19(20-g)+2.60g=35.80

43.8-2.19g+2.60g=35.80

0.41g=35.80-43.8

0.41g=-8

g=-8/0.41

g= -19.51

PaQa+PgQg=35.80

2.19a+2.60(-19.51)=35.80

2.19a-50.726=35.80

2.19a=35.80+50.726

2.19a=86.526

a=86.526/2.19

=39.51

PaA+PgG=35.80

Pa(20-G)+2.60G=35.80

35.80/2.60 = 13.77 pounds of grapes, but no money will be left to buy apples, unless Pa=0

G<13.77

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

24 units

step-by-step explanation: