At a food truck, the cost in dollars of deluxe tacos and standard tacos can be modeled by the equation . If a customer orders exactly deluxe tacos, how many standard tacos can the customer also purchase for dollars in total?

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SAT Linear Equations in Two Variables Question 53 | Free SAT Prep | Aniko

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Question 53·Medium·Linear Equations in Two Variables

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At a food truck, the cost in dollars of $d$ deluxe tacos and $s$ standard tacos can be modeled by the equation $4d + 1.5s = 27$ . If a customer orders exactly $3$ deluxe tacos, how many standard tacos can the customer also purchase for $27$ dollars in total?

For linear cost equations like this, first plug in any given value (here, the number of deluxe tacos) to reduce the equation to one variable. Then solve step by step: simplify the constant term, move constants to the other side, and isolate the remaining variable with division. When decimals appear, you can clear them by multiplying both sides of the equation by a power of 10 or another convenient number to make the arithmetic faster and less error-prone on the SAT.

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Use the information about deluxe tacos

The equation $4d + 1.5s = 27$ uses $d$ for deluxe tacos and $s$ for standard tacos. You are told the customer orders 3 deluxe tacos. How can you show that in the equation?

Reduce the equation to one variable

After substituting the value for $d$ , simplify the equation so it only has $s$ in it. What arithmetic operation should you do with $4$ and the number of deluxe tacos?

Solve for $s$ step by step

Once your equation looks like $12 + 1.5s = 27$ , first move the 12 to the other side, then solve $1.5s =$ ? for $s$ . If decimals are uncomfortable, consider multiplying both sides by 2 to clear the decimal.

Desmos Guide

Use Desmos to compute the remaining tacos

In a Desmos expression line, enter (27 - 4*3) / 1.5. This expression represents the money left after paying for 3 deluxe tacos divided by the cost of one standard taco. The numerical result is the number of standard tacos the customer can buy.

Step-by-step Explanation

Substitute the given number of deluxe tacos

You are told the customer orders exactly $3$ deluxe tacos, so $d = 3$ .

Substitute $d = 3$ into the cost equation:

4d + 1.5s = 27 \\[0.7em] 4(3) + 1.5s = 27

Now the equation has only one variable, $s$ .

Simplify the constant term

Multiply $4(3)$ to simplify the left side:

4(3) + 1.5s = 27 \\[0.7em] 12 + 1.5s = 27

This means the 3 deluxe tacos cost $12, and the rest of the $27 is for standard tacos.

Isolate the term with $s$

Subtract $12$ from both sides to get the part of the money that goes to standard tacos:

12 + 1.5s = 27 \\[0.7em] 1.5s = 27 - 12 \\[0.7em] 1.5s = 15

Now you just need to solve $1.5s = 15$ for $s$ .

Solve for the number of standard tacos and match the choice

Divide both sides by $1.5$ to solve for $s$ :

1.5s = 15 \\[0.7em] s = \frac{15}{1.5}

To avoid decimals, multiply numerator and denominator by $2$ :

s = \frac{15 \cdot 2}{1.5 \cdot 2} = \frac{30}{3} = 10

So the customer can buy $10$ standard tacos. This corresponds to answer choice C) 10.

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Desmos Guide

Step-by-step Explanation

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Desmos Guide

Step-by-step Explanation