MATH SOLVE

3 months ago

Q:
# 1. At a fundraiser dinner, the bill for 4 cups of coffeeand 6 spaghetti specials is $20.50, whereas the bill for 1 cup of coffee and 3 spaghettispecials is $8.75.Writea 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 spaghettispecial.Use thesubstitution method to solve the system of equations.Whatwould the bill be for 1 cup of coffee and 1 spaghetti special?(Pls help!)

Accepted Solution

A:

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 sWe are given that:4 cups of coffee and 6 spaghetti cost $20.5This means that:4c + 6s = 20.5 ................> equation 1We are also given that:1 cup of coffee and 3 spaghetti cost $8.75This means that:c + 3s = 8.75 .................> equation 22- Solving the equations using substitution methods:From equation 2:c = 8.75 - 3s ................> ISubstitute with I in equation 1 and solve for s as follows:4c + 6s = 20.54(8.75 - 3s) + 6s = 20.535 - 12s + 6s = 20.535 - 6s = 20.56s = 14.5s = $2.41667Substitute with s in I to get c:c = 8.75 - 3s c = 8.75 - 3(2.41667) = 1.4999 = $1.53- getting price for 1 cup of coffee and 1 spaghetti:c + s = 1.5 + 2.41667 = $3.91667Hope this helps :)