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# writing systems of Equations from Context

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Jordan and his children went into a restaurant and he bought $26 worth of drinks and tacos. Each drink costs$2.50 and each taco costs \$2. He bought 4 more tacos than drinks. Write a system of equations that could be used to determine the number of drinks and the number of tacos that Jordan bought. Define the variables that you use to write the system.

Jan 10, 2023

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Alright, so we're going to write a system of equations and define the variables:

d = the number of drinks Jordan buys

t = the number of tacos Jordan buys

We know that he bought 4 more tacos than drinks so:

$$t = 4 + d$$

Our next equation is:

$$2.50 \cdot d + 2 \cdot t = 26$$

Since t = 4 + d, we substitute this into our equation:

$$2.50 \cdot d + 2 \cdot (d + 4) = 26$$

We simplify:

$$2.50d + 2d + 8 = 26$$

Subtract 8 from both sides:

$$2.50d + 2d = 18$$

$$4.50d = 18$$

We divide by 4.50

$$d = 4$$

So we know that he bought 4 drinks, and when we do d + 4 = 8 tacos.

If anything is wrong, please tell me as I would be happy to help!

Jan 10, 2023