Question

Maka loves the lunch combinations at Rosita’s Mexican Restaurant. Today however, she wants a different combination than the ones listed on the menu.

If Maka wants 2 and 1 enchilada, how much should she plan to spend.

Short answer

The total amount that Maka needs to spent on 2 burritos and one enchilada is$7.80$.

Step-by-step solution

– First construct a system of equations corresponding to the given situation.

Let $x$be the price of an enchilada, $y$be the price of a taco, and $z$be the price of a burrito.

In the figure, it is given that the total cost of two tacos, and one burrito is %6.55.

So, $2y+z=6.55$.

In the figure, it is given that the total cost of one enchilada, one taco, and one burrito is %7.10.

So, $x+y+z=7.10$

In the figure, it is given that the total cost of 2 tacos and two enchiladas is %8.90.

This can be mathematically written as $2x+2y=8.90$.

So, the system of equations will be:

$\begin{array}{c}2y+z=6.55\\ x+y+z=7.10\\ 2x+2y=8.90\end{array}$

– Use the elimination method to get the system of equations in two variables.

Multiply the $equationx+y+z=7.10$by 2 and subtract the new resultant equation to the equation $2y+z=6.55$.

$\begin{array}{l}\underset{\_}{\begin{array}{l}x+y+z=7.10\\ 2y+z=6.55\end{array}}\begin{array}{c}\text{multiplyby2}\\ \end{array}\underset{\_}{\begin{array}{l}2x+2y+2z=14.20\\ (-)+2y+z=6.55\end{array}}\\ 2x+0+z=7.65\end{array}$

So, the resultant equation is $2x+z=7.65$.

Multiply the $equationx+y+z=7.10$by 2 and subtract the new resultant equation from the equation $2x+2y=8.90$

$\begin{array}{l}\underset{\_}{\begin{array}{l}x+y+z=7.10\\ 2x+2y=8.90\end{array}}\begin{array}{c}\text{multiplyby2}\\ \end{array}\underset{\_}{\begin{array}{l}2x+2y+2z=14.20\\ (-)2x+2y+=8.90\end{array}}\\ 0+0+2z=5.30\end{array}$

So, the resultant equation is $2z =5.30$.

– Solve the system of equations in two variables

Solve $2z =5.30$for $z$:

$\begin{array}{c}2z=5.30\\ \frac{2z}{2}=\frac{5.30}{2}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}dividebothsidesby}2\\ z=2.65\end{array}$

– Find the values of x and y.

Substitute $z=2.65$in $2x+z=7.65$and find the value of $x$.

$\begin{array}{c}2x+z=7.65\\ 2x+2.65=7.65\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Substitute}2.65\text{for}z\\ 2x=5\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Subtract}2.65\text{frombothsides}\\ x=2.5\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Dividebothsidesby2}\end{array}$

Substitute $z=2.65$in $2y+z=6.55$and find the value of $y$

$\begin{array}{c}2y+z=6.55\\ 2y+2.65=6.55\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Substitute}2.65\text{for}z\\ 2y=3.90\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Subtract}2.65\text{frombothsides}\\ y=1.95\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Dividebothsidesby2}\end{array}$

Hence, the solution of the given system of equations is$\left(x,y,z\right)=\left(2.5,1.95,2.65\right)$.

.

– Use the substitution and find the total amount that spent on 2 burritos and one enchilada.

The mathematical expression that gives the total amount of 2 burritos and one enchilada is $2z+x.$

Substitute$x=2.5,z=2.65$in $2z+x.$

$\begin{array}{c}2z+x=2\left(2.65\right)+2.5\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}substitute}2.65\text{for}z,2.5\text{for}x\\ =5.30+2.5\text{simplify}\\ =7.80\end{array}$

Hence, the total amount that Maka needs to spent on 2 burritos and one enchilada is $7.80$.