Expressions and Equations: Using Variables to Represent Numbers and Relationships (CCSS.6.EE.6)
Common Core 6th Grade Math · Learn by Concept
Help Questions
Common Core 6th Grade Math › Expressions and Equations: Using Variables to Represent Numbers and Relationships (CCSS.6.EE.6)
Bike rental costs 6 dollars per hour, plus a one-time 4 dollar helmet fee. Let $x$ be the number of hours.
Which expression represents the situation?
$6 + 4x$
$6x + 4$
$6x - 4$
$6(x + 4)$
Explanation
Per hour means multiply the hourly rate by the number of hours ($6x$), and "plus a one-time 4 dollar helmet fee" means add 4: $6x + 4$. Do not subtract the fee or multiply the fee by $x$.
A taxi charges a 3 dollar starting fee and 2 dollars per mile. Let $m$ be the number of miles.
Which expression represents the situation?
$3m + 2$
$2m - 3$
$2(m + 3)$
$2m + 3$
Explanation
Per mile means multiply the rate by miles ($2m$), and "starting fee" is added once: $+3$. So the expression is $2m + 3$, not $2(m+3)$.
For a field trip, each student pays 5 dollars for admission, and there is a single 12 dollar bus fee for the class. Let $x$ be the number of students.
Which expression represents the situation?
$5x + 12$
$12x + 5$
$5(x + 12)$
$5x - 12$
Explanation
Each student pays 5 dollars means $5x$, and "a single 12 dollar bus fee" means add 12 once: $5x + 12$. Do not multiply the bus fee by $x$.
In a game, you earn 10 points for each level you complete and you start with 15 bonus points. Let $x$ be the number of levels completed.
Which expression represents the situation?
$15x + 10$
$10(x + 15)$
$10x + 15$
$10x - 15$
Explanation
For each level means multiply the points per level by the number of levels ($10x$), and "start with 15 bonus points" means add 15: $10x + 15$.
A music app costs 7 dollars per month plus a one-time 15 dollar sign-up fee. Let $m$ be the number of months you subscribe. Which expression represents the situation?
$7m + 15$
$15m + 7$
$7 + 15m$
$7(m + 15)$
Explanation
Per month means multiply 7 by $m$, and "one-time fee" means add 15, giving $7m + 15$.
A taxi charges a start fee of 3 dollars plus 2 dollars per mile. Let $x$ be the number of miles traveled. Which expression represents the situation?
$3x + 2$
$2(x + 3)$
$5x$
$2x + 3$
Explanation
Per mile means multiply 2 by $x$, and "start fee" means add 3, so $2x + 3$.
A teacher buys $p$ packs of stickers. Each pack has 12 stickers, and there are 5 extra loose stickers. Which expression represents the situation?
$12(p + 5)$
$12p + 5$
$5p + 12$
$12p - 5$
Explanation
Each pack has 12 means multiply 12 by $p$, and "5 extra" means add 5: $12p + 5$.
A smoothie shop charges 4 dollars per smoothie and takes 3 dollars off the total order as a discount. Let $s$ be the number of smoothies. Which expression represents the situation?
$4(s - 3)$
$3s + 4$
$4s - 3$
$4s + 3$
Explanation
Per smoothie means multiply 4 by $s$, and a "discount of 3" means subtract 3: $4s - 3$.