General
General
Easy

Question

This summer, Lara wants to charge 1.5 times as much for mowing and ranking, but her expenses ($ 10 per weekend) will also increase 1.5 times. The expression below can be used to find how much Lara will make this summer mowing and ranking x lawns in a weekend.
Mowing the lawn = $10.50
Ranking the cut grass = $3.5
Hint: 1.5($10.50 x + $3.50 x - 10)

  1. 21x – 15    
  2. 21x    
  3. 21x – 5    
  4. 0    

Hint:

In this question, we are given an algebraic expression for the amount of money Lara is going to make by doing ranking and mowing “x” number of lawns. We have to simplify the equation to get the final value of her earnings.

The correct answer is: 21x – 15


    The given expression is 1.5( 10.5x + 3.5x – 10)
    The above expression is an algebraic expression. The variable in the above expression is ‘x’
    There are three terms in the bracket. The first two terms have the same variable. Such terms with the same variables are called as “like terms”. They can be added to or subtracted from each other. Terms with different variables are unlike term. The third term is a constant.
    Let’s solve the equation step by step.
    First we will add the first two terms inside the bracket with the same variable.
    1.5( 10.5x + 3.5x – 10) = 1.5( 14x – 10)
    Now, the terms inside the bracket are “unlike terms”. So, no further operation is possible.
    To solve further we will use distributive property. It states that the quantity outside the bracket or in multiplication with the bracket can be equally distributed to the terms inside the bracket.
    So we get,
    1.5( 10.5x + 3.5x – 10) = 21x – 15
    As both are unlike terms, no further operation is possible.
    Therefore, the value of the equation is 21x – 15.

    We should know different properties necessary for algebraic expression.

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