Answer to Question #262960 in Algebra for accoitu

Question

2.2 Simphiwe bought meal tickets to use at the school’s cafeteria. Each meal requires 2

tickets, and she bought 14 tickets in total. She has already used some of the tickets, and

she still has some left.

2.2.1 Write four equivalent expressions that gives the number of tickets Simphiwe has

left in terms of x, where x is the number of meals she has already bought. (4)

2.2.2 14 − 2x represents the number of tickets Simphiwe has left after she bought x

meals. How can 14, −2, and 2x be interpreted in terms of tickets and meals? (6)

2.2.3 2(7 − x) also represents the number of tickets Simphiwe has left after she

bought x meals. How can 7, (7 − x), and 2 be interpreted in terms of tickets and

meals? (6)

2.2.4 Discuss the purpose and the importance of the instructional activity in relation to

fostering algebraic reasoning in mathematics education. (4)

Answer 1

2.2.1) 14-2x

2(7-x)

14-x-x

10-2x+4

2.2.2) In the expression 14−2x

, the 14 represents the number of tickets Simphiwe started with since the value of the expression is 14 when x=0

. The −2 represents the number of tickets she spends per meal. 2x

represents the number of tickets she has to subtract from her initial amount after x

meals.

2.2.3) In the expression 2(7−x), the 7 represents the total number of meals Simphiwe can get on. (7−x) represents the number of meals she has left and the 2 represents the number of tickets required for each ride Simphiwe has left.

2.2.4) The purpose of this instructional task is to illustrate how different, but equivalent, algebraic expressions can reveal different information about a situation represented by those expressions. This task can be used to motivate working with equivalent expressions, which is an important skill for solving linear equations and interpreting them in contexts.