Question

At a restaurant the cost for a breakfast taco and a small glass of milk is $5.10 how much is it The cost for two tacos and three small glasses of milk is $11.80 how much is it for a taco

Answer 1

Let x = price of taco

Let y = price of glass of milk

"The cost of a breakfast taco and a small glass of milk is $5.10" translates to

`x+y=5.10`

"The cost for two tacos and three small glasses of milk is $11.80" translates to

`2x+3y=11.80`

We now have the system

`\begin{gathered} x+y=5.10\text{ (first equation)} \\ 2x+3y=11.80\text{ (second equation)} \end{gathered}`

Solve for y using the first equation

`\begin{gathered} x+y=5.10 \\ y=5.10-x\text{ (third equation)} \end{gathered}`

Use the third equation and substitute it to the second equation

`\begin{gathered} 2x+3y=11.80 \\ 2x+3(5.10-x)=11.80 \\ 2x+15.3-3x=11.80 \\ -x=11.80-15.3 \\ -x=-3.5 \\ x=3.5 \end{gathered}`

Substitute the value of x to the third equation and we have

`\begin{gathered} y=5.10-3.5 \\ y=1.6 \end{gathered}`

Since x is the price of taco, the cost of a taco is $3.50.