3.03 Rewriting expressions to understand relationships
Interactive practice questions
In a particular year, Re-source Waste Recovery produces sewage treatment plants at a cost of $\$u$$u per plant. Re-source Waste Recovery also pays a fee of $\$b$$b per year for its use of the production facilities.
Using only addition, write an expression that represents the total production cost from $1$1 year if there are $3$3 sewage treatment plants produced in that year.
Which of the following expressions is also equivalent to the production cost in that year?
$3u+b$3u+b
$3\left(u+b\right)$3(u+b)
$b+b+b+u$b+b+b+u
$bu$bu
A clothing store receives a shipment of jackets and skirts. The jackets come in blue boxes containing $6$6 jackets each, while the skirts come in red boxes containing $5$5 skirts each. In this shipment, there are $x$x blue boxes and $y$y red boxes.
Consider the case when $n$n is even and $m$m is odd.
Xavier travels to a foreign country, where the value of currency is described in terms of the values ‘$x$x’ and ‘$y$y’. When Xavier arrives, he has plenty of coins worth $2y$2y and plenty of notes worth $x+y$x+y, but none of the several other types of coins or notes.
Outcomes
7.EE.2
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.