Chapter 6, Problem 13MCQ

a.

To determine

To define: The variables to represent the cost of a taco and the cost of a burrito.

Answer to Problem 13MCQ

The algebraic quantities x and y are variables that represent cost of one taco and cost of one burrito respectively.

Explanation of Solution

Given:

The cost of two orders at a restaurant is shown in table given below.

Concept used:

The variables are independent quantities.

Definition:

Suppose the cost of one taco is x and cost of one burrito is y . The algebraic quantities x and y are variables.

b.

To determine

To write: A system of equations to find the cost of a single taco and a single burrito.

Answer to Problem 13MCQ

A system of equations to find the cost of a single taco and a single burrito is

  $3x+2y=23.35$

  $4x+y=19.80$ .

Explanation of Solution

Given:

The data table in part (a)

Concept used:

According to the given conditions we connect the variables and given quantities.

Calculations:

Conclusion:

In order-1, the total cost of 3 tacos and 2 burritos is $23.35. The cost of one taco is x and that of burrito is y . So cost of 3 tacos is $ 3x and of 2 burritos is $ 2y . Therefore, the equation that connect the variable and given quantities is

  $3x+2y=23.35$

… (1)

In order-2, the total cost of 4 tacos and 1burritos is $19.80. The cost of one taco is x and that of burrito is y . So cost of 3 tacos is $ 4x and of 2 burritos is $ y . Therefore, the equation that connect the variable and given quantities is

  $4x+y=19.80$

… (2)

Conclusion:

A system of equations to find the cost of a single taco and a single burrito is

  $3x+2y=23.35$

  $4x+y=19.80$ .

c.

To determine

To solve: The system of equations in obtained in part (a).

Answer to Problem 13MCQ

The solution of system of equations is $x=3.25$ and $y=6.8$ . The solution means that cost of one taco is $ 3.35 and the cost of one burrito is $6.80.

Explanation of Solution

Given:

The given system of equations is $3x+2y=23.35$ , $4x+y=19.80$ .

Method used:

We solve equations using graphing calculator.

Graph:

The graph of given system of equations $3x+2y=23.35$ , $4x+y=19.80$ is shown in Figure-1.

We see that lines $3x+2y=23.35$ and $4x+y=19.80$ intersect at point $\left(\mathrm{3.25.6.8}\right)$ , i.e., $x=3.25$

  $y=6.8$ is the solution of system of equations $3x+2y=23.35$ , $4x+y=19.80$ .

The solution means that cost of one taco is $ 3.35 and the cost of one burrito is $6.80.

Conclusion:

The solution of system of equations is $x=3.25$ and $y=6.8$ . The solution means that cost of one taco is $ 3.35 and the cost of one burrito is $6.80.

d.

To determine

To find: The amount to be paid by a customer to buy 2 taco and 2 burrito.

Answer to Problem 13MCQ

The amount to be paid by a customer to buy 2 taco and 2 burrito is $\$20.10$ .

Explanation of Solution

Given:

The cost of one taco is $ 3.35 and the cost of one burrito is $6.80.

Formula used:

Cost of n items C = n × cost of one item.

Calculations:

The amount paid by customer to buy 2 tacos $c_1=2\times \$3.25=\$6.50$ .

The amount paid by customer to buy 2burritos $c_2=2\times \$6.80=\$13.60$ .

Therefore, the amount to be paid by a customer to buy 2 taco and 2 burrito is

  $c_1+c_2=\$6.50+\$13.60=\$20.10$

Conclusion:

The amount to be paid by a customer to buy 2 taco and 2 burrito is $\$20.10$ .