Solve real world problems with a system of linear equations

by jhduHU
(COACIPC)

A burger place sells burgers (b) for $4, and fries (f) for $2. If bob bought six items for a total of $18, how many did he buy of each?


Solution

A system of linear equations can be used to solve this problem.

Let b be the number of burgers bob bought

Let f be the number of orders he placed for French fries

Then, we can come up with the following two equations

4b + 2f = 18 (equation 1)

b + f = 6 (equation 2)

Solve for b in equation 2. We can do this by subtracting f from both sides of the equation

b + f - f = 6 - f

b = 6 - f

Replace b with 6 - f in equation 1

4 (6 - f) + 2f = 18

4x6 - 4xf + 2f = 18

24 - 4f + 2f = 18

24 - 2f = 18

24 - 18 = 2f

6 = 2f

f = 3

Since b = 6 - f, b = 6 - 3 = 3

Therefore, Bob ordered 3 items each