Let e, l and c be the number of espressos, lattes and caf´es cubanos manufactured, and let g, m and s be the amounts of grounds, milk and sugar left over when they are done. Let p be the amount of money they take in. Record the linear equations relating e, l, c, g, m, s and p.

Answer and Explanation:

the given data can be written as follows

                7 kg of coffee ground                  1 gallon milk               10cups of sugar

espressos 8 gms of ground                       0.0625 gallons milk        0.125 cups of sugar

Lattes       15 gms of ground                      no milk                         0.125cups of sugar

CafeCubanos 7.5gms of ground                 no milk                         0.125 cups of sugar

Given that, e represents the espressos, l represents the Lattes, and c represents cafe's cubanos.

Let g represents the amount of grounds, m represents the amount of milk, and s represents the amount of sugar.

price at espressos is $2, and $4 for lattes and $5 for Cafecubanos.

Let p be the amount of money they takein.

Let x , y ,z be the amounts of coffeeground, milk and sugar to be used for manufacture of espressos, lattes and cafcubanos.

So, the matrix form can be written as,

8       0           0           x           e

15 0.0625 0.0125      y    =     l

7.5    0         0.125      z           c

So, this can be written as, 8x+0(y)+0(z)=e

15x+0.0625y+0.125z=l

7.5x+0(y)+0.125z=c

Total left over coffee ground when e=l=c=1 is

(7kg) -(8+15+7.5)=7000-30.5=6969.5

Total left over sugar is, 10 -(0.125+0.125)=1-0.250=0.75

Total left over milk is 1-0.0625=0.9375

So, for one quantitiy that is e=l=c=1, the left over quatitiy will be

6969.5g+9.750s+0.935m

NOw, cost of each espressos is $2

Cost of each lattes is $4 and cost of each cafe cabons is $5

So, p=2e+4l+5c

for e=l=c=0, the price p is 0.

If e=l=c=1, then P=2+4+5=11

Similarly, by giving the values like this, we will get different value at different values of e,l,c

e=8x,

l=15x+0.0625y+0.125z

c=7.5x+0(y)+0.125z

Choose the values of x, y and in such a way that, x<=7000,y<=1,z<=10

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

x=6 and x=3

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