The tape diagram represents an equation with two equal-length tapes. …

Mathematics Questions

The tape diagram represents an equation with two equal-length tapes. The top tape is divided into two parts: one labeled “a” and the other labeled 17. The bottom tape is labeled 35. Write an equation to represent the tape diagram. Is it (a) a – 17 = 35 or (b) a + 17 = 35? Find the value of a that makes the equation true.

Short Answer

The tape diagram illustrates the relationship between two sections, with one part labeled “a” and the other “17”, totaling to “35”. The equation formed is a + 17 = 35, which simplifies to find that a equals 18.

Step-by-Step Solution

Step 1: Understand the Tape Diagram

The tape diagram consists of two sections that represent lengths, where the top tape is divided into two parts: one part is labeled a and the other part is 17. The bottom tape, representing the total length, is labeled 35. This visual representation helps in forming an equation based on the lengths of the tapes.

Step 2: Set Up the Equation

To express the relationship between the two tapes, combine the lengths of the top tape. The equation formed by equating the top and bottom tapes is a + 17 = 35. This shows that the total of the two parts of the top tape is equal to the length of the bottom tape.

Step 3: Solve for “a”

To find the value of a, you need to isolate it in the equation. Subtract 17 from both sides:

  • a + 17 – 17 = 35 – 17
  • This simplifies to a = 18.

Thus, the value of a that satisfies the equation is 18.

Related Concepts

Tape Diagram

A visual representation used to illustrate the relationships between different quantities by segmenting lengths into parts that can be compared.

Equation

A mathematical statement that asserts the equality of two expressions, often used to express relationships among variables.

Isolation

A method in algebra where you manipulate an equation to get one variable by itself on one side, making it possible to solve for that variable.

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