Question

Ron bought 2 hamburgers and 1 soda for $8.75. A hamburger costs $2.50

more than a soda. Write a system of equations which represents this situation
and then solve the system to determine the cost of a hamburger and a soda.

Answer 1

Hamburger: $3.75 each

Soda: $1.25 each

Explanation:

(cost of 2 hamburgers) + (cost of 1 soda) = (total expenditure of $8.75).

Letting s represent the cost of a soda and h the cost of a hamburger in terms of the cost of a soda results in the system

h = s + $2.50

2h + 1s = $8.75

Use the substitution method. In the second equation replace h with s + $2.50:

2(s + $2.50) + 1s = $8.75, or

2s + $5.00 + 1s = $8.75

Then 3s = $3.75, and s = $1.25. A soda costs $1.25.

Since h = s + $2.50, we learn that a hamburger costs $1.25 + $2.50, or $3.75.

Hamburger: $3.75 each

Soda: $1.25 each