Question

If 2 tacos and 3 drinks cost $14, and 3 tacos and 2 drinks cost $16, how much does a taco cost?

Answer 1

Answer:

1 taco is $4

Step-by-step explanation:

2t + 3d = 14              4t + 6d = 28

3t + 2d = 16              -9t -6d = -48

-5t = -20

t = 4

Answer 2

A tacos would cost $2.67.

• Let the cost of tacos be T.

• Let the cost of drinks be D.

Translating the word problem into an algebraic equation, we have;

$2T \; + \; 3D = 14$   ......equation 1

$3T \; + \; 2D = 16$   ......equation 2

To find how much a tacos cost, we would solve the above system of equations by using the substitution method.

From eqn 1, we would make D the subject of formula;

$D = \frac {14 \; - 2T}{3}$  .....equation 3

Substituting eqn 3 into eqn 2, we have;

$3T \; + \; 2(\frac {14 \; - 2T}{3}) = 16\\\\3T \; + \; \frac {28 \; - 24}{3} = 16$

Lowest common multiple (LCM) = 3

$\frac {9T \; + \; 28 \;- \; 4}{3} = 16$

Cross-multiplying, we have;

$9T \; + \; 28 \;- \; 4 = 16 \; * \; 3\\\\9T \; + 24 = 48\\\\9T = 48 \; - 24\\\\9T = 24\\\\T = \frac{24}{9}$

T = $2.67