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There are four different price points on the menu. These are $\$7,$ $\$9,$ $\$5,$ and $\$6.$ If Tadeo and his brother order the same combo, just one of these numbers will satisfy the given equation. With this in mind, substitute each of the prices into the equation, one at a time, and simplify. Start with $\$7.$ Since $x=7$ makes the equation true, it is a solution to the equation. Now, check the remaining prices by substituting them into the equation and simplifying to see whether the equation has more solutions.

Menu	Menu Price	Substitution into $2x+8=22$	Check
Combo I	$7$	$2(7)+8\stackrel{?}{=}22$	$22=22✓$
Combo II	$9$	$2(9)+8\stackrel{?}{=}22$	$26\ne 22\times$
Combo III	$5$	$2(5)+8\stackrel{?}{=}22$	$18\ne 22\times$
Combo IV	$6$	$2(6)+8\stackrel{?}{=}22$	$20\ne 22\times$

As shown in the table, the other prices do not satisfy the equation. This means that Tadeo and his brother both ordered Combo I.

Once again, start with the first combo, which costs $\$7.$ Since $x=7$ does not satisfy the given equation, it is not a solution. This means that neither boy ordered Combo I. Check the remaining combo prices by following the same method.

Menu	Menu Price	Substitution into $x^2-15x=\text{-}54$	Check
Combo I	$7$	$$\begin{gathered} (7{)}^2-15(7)\stackrel{?}{=}\text{-}54 \\ 49-105\stackrel{?}{=}\text{-}54 \end{gathered}$$	$\text{-}56\ne \text{-}54\times$
Combo II	$9$	$$\begin{gathered} (9{)}^2-15(9)\stackrel{?}{=}\text{-}54 \\ 81-135\stackrel{?}{=}\text{-}54 \end{gathered}$$	$\text{-}54=\text{-}54✓$
Combo III	$5$	$$\begin{gathered} (5{)}^2-15(5)\stackrel{?}{=}\text{-}54 \\ 25-75\stackrel{?}{=}\text{-}54 \end{gathered}$$	$\text{-}50\ne \text{-}54\times$
Combo IV	$6$	$$\begin{gathered} (6{)}^2-15(6)\stackrel{?}{=}\text{-}54 \\ 36-90\stackrel{?}{=}\text{-}54 \end{gathered}$$	$\text{-}54=\text{-}54✓$

According to the table, the equation has two solutions, $x=9$ and $x=6.$ This means that one of the brothers ordered Combo II and the other one ordered Combo IV. Bon appetit!

The word is represents an equals sign, which means that the expressions to the left and right sides of this word are equal to each other. Tadeo is $168$ centimeters tall, so write this number on the left-hand side of the equation in place of $\text{Tadeo’s height}.$

Next, more than indicates the addition of numbers. Let $x$ be the variable that represents Dylan's height to write an expression for the right-hand side of the equation.

There may be other ways to write this equation. Saying that Dylan's height is $12$ centimeters less than Tadeo's height has the same meaning. Here, less than refers to subtraction. Consider how to rewrite the equation as a subtraction expression. Both of the equations can be used to find Dylan's height. Dylan's weight can be found by using the translated equation. Note that there are other possible ways to write the fraction $\frac{3}{4}.$ This means that the equation $x=0.75\times 52$ also represents the given sentence. This situation can also be represented by other equations. If Tadeo is $3$ years older than Dylan, we know that his age is Dylan's age plus $3.$ This means that the equation can be written using addition as well. Both equations can be used to find Dylan's age. Also, keep in mind that there is not only one way to represent a situation by an equation. Equations can be rewritten as several different equations by rearranging the terms of the equation.

Now simplify the equation to find how many cards he had. This means that Dylan had $18$ collectible cards before buying more at the mall. This also means that $n=18$ is the solution to the equation. Let $m$ be the initial money. Substitute the given amounts into this model to write an equation. Now simplify the equation. The solution to the equation is $47,$ so Tadeo had $\$47$ before buying the games.

The store paid the boys the same amount of money for each toy car. Since the boys received $12$ times the amount of money paid per car to get $\$36,$ the amount of money the boys were paid per car $x$ can be found by dividing $36$ by $12.$ Now simplify the equation to find how much the boys were paid for each toy car they sold. Since $x$ represents the amount of money the boys receive per toy car, this means that the shop paid the boys $\$3$ for each toy car. This number is also the solution to the equation. Consider how to split $\$54$ in groups of $\$3.$ This will require division — in other words, divide the total amount that will be earned by the price of a single car to find the number of cars sold. Let $y$ be the number of cars. Now calculate the quotient to find the value of $y.$ This means that they need to sell $18$ toy cars to get $\$54.$ Keep in mind that the scenarios from Part A and Part B can be solved by using other methods. These solutions are just examples of one way of how to find the required information.

After the boys got in the elevator, it first went up $3$ floors, then down $7$ floors. Start by drawing a diagram to represent this situation.

Keep in mind that the ground floor is represented as Floor $1.$ Since the boys went $7$ floors down before getting off the elevator, they must be at the $1+7=8^{\text{th}}$ floor after going $3$ floors up.

Recall that the boys reached the $8^{\text{th}}$ floor after going $3$ floors up. This means that they must be at a floor that $3$ floors down from the $8^{\text{th}}$ floor when they get in the elevator. Write this situation as an equation. Now simplify this equation to find the floor the boys were on when they got in the elevator. This means that the boys got into the elevator on Floor $5.$ Notice that this is also the solution to the equation.