if 3 tacos and 2 burriots cost $7.40 and 4 tacos and 1 burrito cost $6.45. Then write a system of equations for the cost of a single taco and a single burrito

Question

Define the variables, explain the solution.

Answer 1

To set up the system of equations we need to define variables for Tacos and Burritos 

 

Let x= tacos

Let y = burritos

 

Now if 3 tacos and 2 burritos cost $7.40  set up the equation as 3x + 2y = 7.40

If 4 tacos and 1 burritos costs $6.45 set up this equation as 4x + y = 6.45

 

So we now have the system:

 

3x + 2y = 7.40

4x + y  = 6.45

 

so we will use elimination to solve this system.  We need to eliminate one of the variables, either the x or the y.  In this case I'll eliminate the y by multiplying the second equation by -2

 

 3x + 2y = 7.40
-2(4x + y = 6.45)

 

after multiplying the second equation by -2 we will get the following:

 

3x + 2y = 7.40
-8x - 2y = -12.90

 

Now I notice that if I add the two equations together the y's will cancel out. (because 2y + (-2y) = 0)

 

3x + 2y = 7.40

 

plus

-8x - 2y = -12.90

 

gives me 

 

-5x = -5.50

 

divide both sides of the equation by -5 to isolate the variable (to get x by itself)

 

x = 1.10

 

now remember x represent Tacos so it cost $1.10 for every Taco.

Now lets solve for y to find out how much a burrito cost.

 

Go back to the original system of equations and choose either the first equation or the second equation to substitute $1.10 for the x value in order to solve for the y value.

 

 I'll use the 2nd equation because it seems easier to evaluate (you could use either equation, whichever seems easier to use TO YOU is the equation you use.  To me the 2nd equation seemed easier so I will use that one)

 

4x + y = 6.45

 

substitute (replace) x with the value we got for x which was 1.10 and solve for y

 

4x + y = 6.45

 

4(1.10) + y = 6.45

 

4.40 + y = 6.45

 

subtract 4.40 from both sides

 

y = 2.05  so it costs $2.05 for every burrito

 

so x = 1.10 and y = 2.05 but you're not done yet.  You now MUST CHECK to see if your solutions for x and y satisfy both equations.  so substitute your values for x and y into both equations and see if they equal 7.40 for the 1st equation and 6.45 for the 2nd equation.

 

here is the original system

3x + 2y = 7.40
4x + y = 6.45

 

substitute x and y into both equations in the system

 

3(1.10) + 2(2.05) = 7.40
4(1.10) + 2.05 = 6.45

 

after evaluating 3(1.10) + 2(2.05) you will get 7.40 so your solution for x and y satisfy this equation.

after evaluating 4(1.10) + 2.05 you will get 6.45 so your solution for x and y satisfy the second equation as well.

 

So a single Taco costs $1.10 and a single burrito costs $2.05

Answer 2

3 tacos + 2 burritos = $7.40

4 tacos + 1 burrito = $6.45

 

lets call tacos t and burritos b. so:

 

 3t+2b = $7.40

4t+1b=$6.45

 

this becomes a substitution problem.  Let's re-write the second equation as:

1b= $6.45 - 4t

 

then, wherever we see a b in the first equation, we will substitute in "$6.45-4t"

 

so 3t+2b=$7.40  becomes

 

3t+2($6.45-4t)=$7.40

3t+$12.90-8t=$7.40

-5t = -$5.5

t= - $5.5/-5 = $1.10

 

Now, we will go back to the second equation and wherever we see a "t", we will substitute in $1.10

 

so 4t + 1b = $6.45 becomes:

4($1.10)+1b=$6.45

$4.40+1b=$6.45

b=$2.05

Answer 3

3T + 2B=7.40

4T+B=6.45

 

To solve you isolate the B variable in the second equation. B=6.45-4T

Then you substitute 6.45 -4T for B in the first equation.

 

3T + 2(6.45-4T)=7.40

Then solve for T.

3T+12.90-8T=7.40

-5T=-5.5

T=1.10 this is the price of one taco.

 

Then substitute 1.10 for T.

3(1.10) +2B=7.40

3.30 + 2B=7.40 

2B=4.10

B=2.05

 

 

When you use one equation to find the value of the variable, check your answer with the other equation: 4(1.10) + 2.05=6.45

 

Answer 4

 System of Equation: 

 

 3 T + 2 B = 7.40

 4T  + 1B  = 6.45

 

Solution by elimination method:

   3 T + 2B = 7.40

-2 ( 4 T + 1B = 6.45)

   -5 T = 7.40 - 12.90 = -5.5

 

       T = -5.5  = $ 1.10   Cost of a Taco

            - 5 

 

     Substitute back into first equation;

     

       3 ( 1.1 ) + 2B = 7.40

 

        2B = 7.40 - 3.30 = 4.10

 

        B = 4.10 =$ 2.05   Cost of a Burito

                2  

Answer 5

If we establish two variables:

 

t - the cost of a taco

b - the cost of a burrito

 

Then we would have these two equations:

 

3t + 2b = 7.40

4t + b = 6.45

 

Solving for t and b gives the cost of a single item. I would start with the second equation, and multiply both sides by 2:

 

8t + 2b = 12.90

 

Then, subtract the first equation:

 

  8t + 2b = 12.90

- (3t + 2b) = 7.40

--------------------

5t = 5.50

t = 1.1

 

Substitute 1.1 for t in either equation to solve for b:

4t + b = 6.45

4(1.1) + b = 6.45 (substitute 1.1 for t)

4.4 + b = 6.45     (remove parentheses)

b = 2.05              (subtract 4.4 from both sides)

 

Burritos cost $2.05, and tacos cost $1.10.

 

Check by plugging values into any equation we have:

3t + 2b = 7.40

3(1.10) + 2(2.05) = 7.40

3.30 + 4.10 = 7.40

7.40 = 7.40

Answer 6

x = cost of one taco in pennies

 

y = cost of one burrito in pennies

 

3x + 2y = 740

 

4x + 1y = 645 => y = 645 - 4x

 

3x + 2(645 - 4x) = 740

 

3x - 8x + 1290 = 740

 

550 = 5x

 

x = 110

 

y = 645 - 4(110)

 

y = 645 - 440

 

y = 205

 

Cost of single toco is $1.10 and single burrito $2.05.

 

check:

 

3(110) + 2(205) =? 740

330 +410

740 = 740 √

 

4(110) + 1(205) =? 645

440 + 205 =? 645

645 = 645 √

Answer 7

let x=cost of a taco

let y=cost of a burrito

3x+2y=$7.40

4x+y=$6.45

multiply the second equation by 2(both sides, all terms)

8x+2y=$12.90

3x+2y=$7.40

now subtract the equations

5x=$5.50

x=$1.10 for the cost of one taco

now substitute

3($1.10)+2y=$7.40

$3.30+2y=$7.40

2y=$4.10

y=$2.05 for the cost of one burrrito