Question

Set-up and solve the following algebraically:
A group of 7 students go out for lunch. If two students have hamburgers and five students have hot dogs, the bill will be $18.75. If five students have hamburgers and two students have hot dogs, the bill
will be $23.25. What is the price of a hamburger?​

Answer 1

Given - Number of students - 7

Cost If two students have hamburgers and five students have hot dogs - $18.75.

Cost If five students have hamburgers and two students have hot dogs - $23.25.

Find - The price of hamburger.

Solution - Let the price of hamburger be $x and the price of hot dogs be $y.

In the first case, 2x + 5y = $18.75. Let this be equation 1.

In the second case, 5x + 2y = $23.25. Let this be equation 2.

Multiplying equation 1 with 2 and equation 2 with 5.

So, new equation will be - equation 3 -> 4x + 10y = 37.5 and equation 4 -> 25x + 10y = 116.25

Solving the new equations -

Substract equation 3 from equation 4.

25x + 10y = 116.25

- (4x + 10y = 37.5)

Result will be 21x = 78.75

So, X = $3.75.

Hence, the price of hamburger is $3.75.