A group of Mayfield students goes out to lunch. If two have burritos and five have tacos, the bill will be $19.50. If five have burritos and two have tacos, the bill will be $22.50. Find the price of a taco and the price of a burrito.

Therefore, the burritos cost $3.50 each and the tacos cost $2.50 each.

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Step-by-step explanation:

Let x denote the price of the burrito and y denote the price of the taco.

Note that two burritos and five tacos cost 2x + 5y and five burritos and two tacos cost 5x + 2y. Since, they cost $19.50 and $22.50, respectively:

2x + 5y = 19.5. . . . . . . . . . . . . . . . . . . . .(1)

5x + 2y = 22.5. . . . . . . . . . . . . . . . . . . . .(2)

Multiplying (1) by 5:

5(2x + 5y) = 5(19.5)

==> 10x + 25y = 97.5. . . . . . . . . . . . . . . . .(3)

Multiplying (2) by 2:

2(5x + 2y) = 2(22.5)

==> 10x + 4y = 45. . . . . . . . . . . . . . . . . . .(4)

Subtracting (4) from (3):

(10x + 25y) - (10x + 4y) = 97.5 - 45

==> 21y = 52.5

==> y = 2.5.

Substituting y = 2.5 in (4) gives:

10x + 10 = 45 ==> x = 3.5.

4x and 6y

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step-by-step explanation: