Question

Jaxon has $65 in his savings account. He deposits $15 every week. His father also deposits $25 into the account every time Jaxon mows the lawn. His savings account balance can be shown with the following expression: 65 + 15w + 25m
Part A: Identify a coefficient, a variable, and a constant in this expression. (3 points)

Part B: If Jaxon saves for 20 weeks and mows the lawn 3 times, how much will he have in his account? Show your work to receive full credit. (4 points)

Part C: If Jaxon had $75 in his savings account, would the coefficient, variable, or constant in the expression change? Why? (3 points)

Answer 1

Part A:
In the expression given, 65 + 15w + 25m: 65 = constant; 15 and 25 = coefficients; w and m = variables.  
Thus, to define:
Constant is a number which the value is already fixed.
Variable is the unknown value in the algebraic expression.
Coefficient is a number which is placed before a variable that indicates how many times the variable is to be multiplied.

65 + 15w + 25m 
65 = 15 (1) + 25 (2)

Part B:
Let x be the savings account balance
W = # of weeks
M = frequency of mowing the lawn  

First, let’s use the expression given above: 15w + 25m.
Since we are solving for a constant, only the variables and coefficient of the expression given are to be used.  
Then, we substitute the variables’ corresponding values.
X = 15 (20) + 25 (3)
Therefore, the savings deposits will amount to:
X = 300 + 75 X = $375  

Part C:
$75 + w + 3m  
Constant will be $75.
Variables: w = no weekly deposit, m = 3
Coefficients: w = 1, m = remains at 25  

This is because we need to adjust the variables and coefficients to solve for the constant.