Question

At Danny’s Diner, the bill at one table for three cups of coffee and five omelets is $7.60. The bill at another table for one cup of coffee and two omelets is $2.90.
a. Create a system of equations to model this problem if c represents the price of a cup of coffee and o represents the price of an omelet.
b. Use she substitution method to solve for the price of each item.
c. Determine how much it would cost to buy one cup of coffee and one omelet

Answer 1

Let a cup of coffee be represented by = c

Let an omelet be represented by = o

Part A:

The bill at one table for three cups of coffee and five omelets is $7.60.

So equation is : $3c+5o=7.60$    ...(1)

The bill at another table for one cup of coffee and two omelets is $2.90.

So, equation is : $1c+2o=2.90$   ...(2)

From equation (2) we get $c=2.90-2o$  .... (3)

Part B:

Substituting the value of 'c' from equation (3) in (1)

$3(2.90-2o)+5o=7.60$

$8.7-6o-5o=7.60$

$o=1.10$

As c=2.90-2o

$c=2.90-2(1.10)$

$c=2.90-2.20=0.70$

Part C:

Hence, cost of 1 cup of coffee is $0.70

Cost of 1 omelet is $1.10