Christopher went into a restaurant and bought 5 hamburgers and 10 drinks, costing a total of $52.50. Wyatt went into the same restaurant and bought 2 hamburgers and 9 drinks, costing a total of $31. Write a system of equations that could be used to determine the price of each hamburger and the price of each drink. Define the variables that you use to write the system.

Answer: Hamburger: $6.5

Drink; $2

Step-by-step explanation:

Hi, we have to write an equation for each one

Christoper

5h + 10d = $52.50

Where:

h = price of a hamburger

d = price of a drink

Wyatt:

2h + 9d = $31

Now we have the system of equations:

5h+10d=52.50 (1)

2h+9d=31 (2)

Isolating "h" from (1)

5h = 52.50 - 10d

h = (52.50 - 10d) / 5

h = 10.5 - 2d

Replacing "h" in (2)

2h+9d=31

2 (10.5-2d) + 9d=31

21 - 4d + 9d=31

-4d+9d=31-21

5d = 10

d = 10/5

d = $2

Finally, replacing d in (1)

5h+10d=52.50

5h+10 (2) = 52.50

5h+20=52.50

5h=52.50-20

5h=32.50

h = 32.50/5

h=$6.5