Question

Three tacos and two burritos cost 653 tacos and one burrito cost 550 how much is one taco

Answer 1

Let T be the price of one taco, and B be the price of one burrito.

Since 3 tacos and 2 burritos cost $6.50, then:

`3T+2B=6.5`

Since 3 tacos and 1 burrito cost $5.50, then:

`3T+B=5.5`

Substract the second equation from the first equation. Left hand side minus left hand side equals right hand side minus right hand side:

`\begin{gathered} (3T+2B)-(3T+B)=6.5-5.5 \\ \Rightarrow3T+2B-3T-B=1 \\ \Rightarrow3T-3T+2B-B=1 \\ \Rightarrow0+B=1 \\ \Rightarrow B=1 \end{gathered}`

Substitute B=1 into the second equation and isolate T to find the price of one taco:

`\begin{gathered} 3T+B=5.5 \\ \Rightarrow3T+1=5.5 \\ \Rightarrow3T=5.5-1 \\ \Rightarrow3T=4.5 \\ \Rightarrow T=(4.5)/(3) \\ \therefore T=1.5 \end{gathered}`

Therefore, the cost of one taco is $1.50.