Answer :
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
A tacos would cost $4.00.
- Let the cost of tacos be T.
- Let the cost of drinks be D.
Translating the word problem into an algebraic equation, we have;
[tex]2T \; + \; 3D = 14[/tex] ......equation 1
[tex]3T \; + \; 2D = 16[/tex] ......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;
[tex]D = \frac {14 \; - 2T}{3}[/tex] .....equation 3
Substituting eqn 3 into eqn 2, we have;
[tex]3T \; + \; 2(\frac {14 \; - 2T}{3}) = 16\\\\3T \; + \; \frac {28 \; - 4T}{3} = 16\\\\[/tex]
Lowest common multiple (LCM) = 3
[tex]\frac {9T \; + \; 28 \;- \; 4T}{3} = 16\\\\\\[/tex]
Cross-multiplying, we have;
[tex]9T \; + \; 28 \;- \; 4T = 16 \; * \; 3\\\\5T \; + 28 = 48\\\\5T = 48 \; - 28\\\\5T = 20\\\\T = \frac{20}{5} \\[/tex]
Tacos, T = $4.00
Therefore, the cost of a tacos is $4.00.
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