Question

1.     At a fundraiser dinner, the bill for 4 cups of coffee

and 6 spaghetti specials is $20.50, whereas the bill for 1 cup of coffee and 3 spaghetti
specials is $8.75.




Write
a system of 2 equations to model this problem. Let c stand for the price of a cup of coffee and let s stand for the price of a spaghetti
special.

Use the
substitution method to solve the system of equations.

What
would the bill be for 1 cup of coffee and 1 spaghetti special?
(Pls help!)

Answer 1

1- Writing the system of equations:

The price of a cup of coffee is denoted by c while the price of a spaghetti is denoted by s

We are given that:

4 cups of coffee and 6 spaghetti cost $20.5

This means that:

4c + 6s = 20.5 ................> equation 1

We are also given that:

1 cup of coffee and 3 spaghetti cost $8.75

This means that:

c + 3s = 8.75 .................> equation 2

2- Solving the equations using substitution methods:

From equation 2:

c = 8.75 - 3s ................> I

Substitute with I in equation 1 and solve for s as follows:

4c + 6s = 20.5

4(8.75 - 3s) + 6s = 20.5

35 - 12s + 6s = 20.5

35 - 6s = 20.5

6s = 14.5

s = $2.41667

Substitute with s in I to get c:

c = 8.75 - 3s

c = 8.75 - 3(2.41667) = 1.4999 = $1.5

3- getting price for 1 cup of coffee and 1 spaghetti:

c + s = 1.5 + 2.41667 = $3.91667

Hope this helps :)