Question

At a particular fast food restaurant, tacos cost $1.29 and

burritos cost $2.19. Michael spent a total of $42.93 at the
restaurant to buy food for a party. If he purchased half as
many burritos as tacos, how many tacos did he buy?

Answer 1

`\displaystyle 18`

Explanation:

we are given that,

1. tacos cost $1.29
2. burritos cost $2.19
3. Michael spent a total of $42.93
4. he purchased half as many burritos as tacos

let the number of tacos and burritos be t and b respectively

according to the 3rd condition we get:

`\displaystyle 1.29t + 2.19b = 42.93`

according to the 4th condition we obtain:

`\displaystyle t = 2b`

therefore our system of linear equation is

`\begin{cases}\displaystyle t=2b \\ \displaystyle 1.29t + 2.19b = 42.93\end{cases}`

so now we end up with a system of linear equation in order to solve the equation we can consider substitution method

so substitute the value of t which yields:

`\displaystyle 1.29 \cdot 2b+ 2.19b = 42.93`

simplify multiplication:

`\displaystyle 2.58b+ 2.19b = 42.93`

since we have same variable we can consider the like terms:

`\displaystyle 4.77b = 42.93`

divide both sides by 4.77:

`\displaystyle (4.77b )/(4.77)= ( 42.93)/(4.77)`

reduce fraction:

`\displaystyle \bcancel{ (4.77b )/(4.77)}= \cancel \frac{ \stackrel{ \large9}{ 42.93}}{4.77}`

`\displaystyle b = 9`

now substitute the value of b:

`\displaystyle t = 2.9`

simplify multiplication:

`\displaystyle t =18`

hence,

he bought 18 tacos

Answer 2

9 burritos and 18 tacos

Explanation:

We can start this problem by assigning a variable to our unknowns.

Let's name x the number of burritos he buys.

The question states he buys half as many burritos as tacos.

Therefore, the number of tacos he bought is 2x.

Let's set up an equation.

(Cost of burrito)(number of burritos)+(Cost of taco)(number of tacos)=Total Cost

2.19x+1.29(2x)=42.93

Simplify

2.19x+2.58x=42.93

4.77x=42.93

x=9

Michael bought 9 burritos.

2*9=18

Michael bought 18 tacos.