Mathematics

Question

Ellen has $75 in her savings account. She deposits $25 every week. Her father also deposits $35 into the account every time Ellen mows the lawn. Her savings account balance can be shown with the following expression:

75 + 25w + 35m

Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)

Part B: If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account? Show your work to receive full credit. (4 points)

Part C: If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)

2 Answer

  • A: coefficient 75, variable 35m, constant 25w
    B: 25x8= 200+70 = 270
    C: coefficient because instead of 75 it would be 95 changing the equation 
  • Answer:

    Part (A) 25 and 35 are the coefficients, m and w are the variables and  75 is the Constant term.

    Part (B) She have $345 in her account if she saves for 8 weeks and mows the lawn 2 times.

    Part (C) the constant term of the expression will change.

    Step-by-step explanation:

    Consider the provided expression.

    75 + 25w + 35m

    Numbers appear with variables are called coefficients.

    Alphabets in an expression are called variables.

    Numbers appear without variables are called Constant terms.

    Part (A) Identify a coefficient, a variable, and a constant in this expression.

    From the above definition variables are the alphabets in an expression,

    m and w are the variables in the expression.

    From the above definition coefficient are number appears with alphabets,

    The number 25 and 35 appear with variable m and w respectively.

    Thus, 25 and 35 are the coefficients.

    From the above definition constant terms are number appears without variables,

    The number 75 appear without variables.

    Thus, 75 is the Constant term.

    Part (B) If Ellen saves for 8 weeks and mows the lawn 2 times, how much will she have in her account.

    Substitute the value of w=8 and m=2 in the provided expression.

    75 + 25(8) + 35(2)

    75 + 200 + 70 = 345

    Hence, she have $345 in her account.

    Part (C) If Ellen had $95 in her savings account, would the coefficient, variable, or constant in the expression change

    $75 in original expression represents the constant term which was the amount in her savings account.

    If she had $95 in her account then the expression will be:

    95 + 25w + 35m

    We can observed that only constant term of the expression change.

    Thus, the constant term of the expression will change, although coefficient and variable will remains unchanged.

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