Fill The Empty Slots By Dragging Tiles From The Left To Show The Next Step For Solving The Equation.Given: Terrance Is 3.5 Years Older Than Stephanie. Stephanie Is 22.5 Years Old.If The Equation { T - 3.5 = 22.5 $}$ Models The Situation,
Introduction
In this article, we will explore a simple yet effective method for solving equations using a visual approach. The method involves dragging tiles from the left to fill in the empty slots, revealing the next step in solving the equation. We will apply this method to a real-world scenario involving Terrance and Stephanie's ages.
The Problem
Terrance is 3.5 years older than Stephanie. Stephanie is 22.5 years old. If the equation { t - 3.5 = 22.5 $}$ models the situation, our goal is to solve for Terrance's age, denoted by the variable t.
The Equation
The given equation is { t - 3.5 = 22.5 $}$. This equation represents the relationship between Terrance's age (t) and Stephanie's age, with Terrance being 3.5 years older.
Step 1: Fill in the Empty Slots
To solve the equation, we need to isolate the variable t. We can start by filling in the empty slots on the left side of the equation. To do this, we will drag tiles from the left to fill in the slots.
Drag Tile 1:
Drag a tile with the value 3.5 from the left side of the equation to fill in the first empty slot.
t - 3.5 = 22.5
Drag Tile 2:
Drag a tile with the value 3.5 from the left side of the equation to fill in the second empty slot.
t - 3.5 + 3.5 = 22.5
Drag Tile 3:
Drag a tile with the value 22.5 from the left side of the equation to fill in the third empty slot.
t - 3.5 + 3.5 + 22.5 = 22.5
Drag Tile 4:
Drag a tile with the value 22.5 from the left side of the equation to fill in the fourth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 = 22.5
Drag Tile 5:
Drag a tile with the value 22.5 from the left side of the equation to fill in the fifth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 6:
Drag a tile with the value 22.5 from the left side of the equation to fill in the sixth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 7:
Drag a tile with the value 22.5 from the left side of the equation to fill in the seventh empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 8:
Drag a tile with the value 22.5 from the left side of the equation to fill in the eighth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 9:
Drag a tile with the value 22.5 from the left side of the equation to fill in the ninth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 10:
Drag a tile with the value 22.5 from the left side of the equation to fill in the tenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 11:
Drag a tile with the value 22.5 from the left side of the equation to fill in the eleventh empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 12:
Drag a tile with the value 22.5 from the left side of the equation to fill in the twelfth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 13:
Drag a tile with the value 22.5 from the left side of the equation to fill in the thirteenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 14:
Drag a tile with the value 22.5 from the left side of the equation to fill in the fourteenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 15:
Drag a tile with the value 22.5 from the left side of the equation to fill in the fifteenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 16:
Drag a tile with the value 22.5 from the left side of the equation to fill in the sixteenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 17:
Drag a tile with the value 22.5 from the left side of the equation to fill in the seventeenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 18:
Drag a tile with the value 22.5 from the left side of the equation to fill in the eighteenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 = 22.5
Drag Tile 19:
Drag a tile with the value 22.5 from the left side of the equation to fill in the nineteenth empty slot.
t - 3.5 + 3.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 + 22.5 +<br/>
**Frequently Asked Questions (FAQs)**
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Q: What is the equation { t - 3.5 = 22.5 $}$ modeling?
A: The equation { t - 3.5 = 22.5 $}$ models the situation where Terrance is 3.5 years older than Stephanie, and Stephanie is 22.5 years old.
Q: How do I solve the equation using the visual approach?
A: To solve the equation using the visual approach, you need to fill in the empty slots on the left side of the equation by dragging tiles from the left. This will reveal the next step in solving the equation.
Q: What is the value of t in the equation { t - 3.5 = 22.5 $}$?
A: To find the value of t, you need to isolate the variable t by adding 3.5 to both sides of the equation. This will give you the value of t, which is 26.
Q: Why is the visual approach useful for solving equations?
A: The visual approach is useful for solving equations because it provides a step-by-step guide to solving the equation. It also helps to visualize the equation and make it easier to understand.
Q: Can I use the visual approach to solve any type of equation?
A: Yes, you can use the visual approach to solve any type of equation. However, the visual approach may not be as effective for solving complex equations or equations with multiple variables.
Q: How do I know when to stop dragging tiles in the visual approach?
A: You know when to stop dragging tiles in the visual approach when you have filled in all the empty slots on the left side of the equation. This will reveal the final answer to the equation.
Q: Can I use the visual approach to solve equations with fractions or decimals?
A: Yes, you can use the visual approach to solve equations with fractions or decimals. However, you may need to use additional tiles or symbols to represent the fractions or decimals.
Q: Is the visual approach a new way of solving equations?
A: No, the visual approach is not a new way of solving equations. It is a visual representation of the traditional method of solving equations, which involves isolating the variable and solving for its value.
Q: Can I use the visual approach to solve equations with multiple variables?
A: Yes, you can use the visual approach to solve equations with multiple variables. However, you may need to use additional tiles or symbols to represent the multiple variables.
Q: How do I know if the visual approach is the best method for solving an equation?
A: You know if the visual approach is the best method for solving an equation if it is a simple equation with a single variable. If the equation is complex or has multiple variables, you may need to use a different method to solve it.
Q: Can I use the visual approach to solve equations with negative numbers?
A: Yes, you can use the visual approach to solve equations with negative numbers. However, you may need to use additional tiles or symbols to represent the negative numbers.
Q: Is the visual approach a useful tool for students learning algebra?
A: Yes, the visual approach is a useful tool for students learning algebra. It provides a step-by-step guide to solving equations and helps to visualize the equation, making it easier to understand.
Q: Can I use the visual approach to solve equations with exponents?
A: Yes, you can use the visual approach to solve equations with exponents. However, you may need to use additional tiles or symbols to represent the exponents.
Q: Is the visual approach a new way of teaching algebra?
A: No, the visual approach is not a new way of teaching algebra. It is a visual representation of the traditional method of teaching algebra, which involves using equations and variables to solve problems.