SOLUTION: A department store sells a pair of shoes for $73 and an assortment of bags for $44 each. In one day, the store sells n pairs of shoes and (n

SOLUTION: A department store sells a pair of shoes for $73 and an assortment of bags for $44 each. In one day, the store sells n pairs of shoes and (n - 7) bags. Which expressions represen

Question 1208927: A department store sells a pair of shoes for $73 and an assortment of bags for $44 each. In one day, the store sells n pairs of shoes and (n - 7) bags. Which expressions represent the day’s total sales for shoes and bags at the store?

73n + 44n + 308

44(n - 7) + 73n

44n + 73(n - 7)

73n + 44(n - 7)

n(73 + 44) - 7

117n - 308
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.

73n + 44(n-7) and everything which is equivalent to it.

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Answers:
73n + 44(n - 7)
44(n - 7) + 73n
117n - 308

Reason
n = number of pairs of shoes
p = 73n = cost of just those shoes alone, when each pair sells at $73
n-7 = number of bags
q = 44(n-7) = cost of just those bags alone, when each bag sells at $44
shoes + bags = p+q = 73n + 44(n - 7) = total cost of shoes and bags
Since we can add two numbers in any order, it means the order of 44(n-7) and 73n doesn't matter. We can swap the order of p and q.
Therefore that expression in red is equivalent to 44(n - 7) + 73n
When distributing and combining like terms, you'll end up with 117n - 308

A visual way to verify if two algebraic expressions are equivalent is to graph them.
Consider graphing y = 73x+44(x-7) and y = 117x-308. Both will produce the exact same line. One line is perfectly overlapping the other.
I recommend using either GeoGebra or Desmos as a graphing tool.
Make sure that you use x instead of n.

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