Liam is a rewards member at a local restaurant. He can buy four tacos at regular price and get 5.50 off of his purchase. Zachary found a coupon to buy three tacos at regular price and get 6.50 off his total. What would the taco price x need to be in order for Liam and Zachary to spend the same amount?

Liam can buy 4 tacos at regular price and get 5.50 off of his purchase while Zachary can buy 3 tacos at regular price and get 6.50 off his total.

There is no price of the taco that makes that both of them spend the same.

Liam and Zachary buy tacos at the same place. Let "x" be the price of each taco and "y" be the total amount spent.

Liam can buy 4 tacos at regular price and get 5.50 off of his purchase.

We can represent the situation through the following linear equation.

y = 4x - 5.50   [1]

Zachary found a coupon to buy three tacos at regular price and get 6.50 off his total.

We can represent the situation through the following linear equation.

y = 3x - 6.50   [2]

We want to know the prices of the taco so that both of them spend the same amount.

We calculate it making [1] equal to [2].

4x - 5.50 = 3x - 6.50

4x - 3x = -6.50 + 5.50

x = -1.00

The taco would have cost -1.00 for both of them to spend the same. Since in reality, this is unlikely, we can say that there is no price of the taco that makes that both of them spend the same.

Liam can buy 4 tacos at regular price and get 5.50 off of his purchase while Zachary can buy 3 tacos at regular price and get 6.50 off his total.

There is no price of the taco that makes that both of them spend the same.

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is there supposed to be a picture here?