Question

I went to my favorite taco stand with some friends. Between us we bought 6 tacos and 2 burritos, and I noticed that the ratio of the amount we spent on tacos to the amount we spent on burritos was 7:4. Later we went back and bought 4 tacos and 3 burritos and spent 1 dollar less. How much money did we spend that time?

Answer 1

$32

Explanation:

First, we'll use the given relations to find the costs of a taco and burrito, then we'll compute the bill for the second visit to the taco stand.

Let t represent the cost of a taco, and b represent the cost of a burrito. The first trip to the taco stand resulted in costs that have the relation ...

(6t)/(2b) = 7/4

Multiplying by 4b, we get ...

12t = 7b . . . . . [eq1]

On the second trip to the taco stand, the costs have the relation ...

(4t +3b) = (6t +2b) -1 . . . . . . subtracting 2b+4t from both sides gives ...

b = 2t - 1 . . . . . [eq2]

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Substituting the expression for b in [eq2] into [eq1], we get ...

12t = 7(2t -1)

0 = 2t -7

7/2 = t = 3.5

b = 2t -1 = 6

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The spending on the second trip was ...

4t +3b = 4(3.5) +3(6) = 32 . . . . dollars