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)
Part
A: <span>In
the expression given, 65 + 15w + 25m: 65 =
constant; 15 and 25 = coefficients; w and m = variables.</span>
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.
The base fee is 4 dollars, and the thing the at changes is x or the hours so the equation is 4 + 2x equals 12. and to solve for x we have to first subtract both sides by 4, getting 2x equals 8 then we divide both sides by 2 to get x equals 4 or 4 hours