A one-variable equation uses one letter to describe related unknown counts. When a story gives several groups and one total, write an expression for each group before adding them. If one group is a multiple of another, multiply that whole group, including any added amount. Multiplying only the letter is a tempting slip.
Hints
- Hint 1
The variable counts small cartons. Nine more means adding to that count. What expression counts the medium cartons?
- Hint 2
The word times calls for multiplication. Multiply the entire medium count by , not only its . Parentheses can show exactly what the multiplies.
- Hint 3
An equation sets two amounts equal. Add the counts for all three sizes and set their sum equal to the given total. Then combine terms to find the matching equation.
Step-by-step
Count each carton size
Step 1Express the medium count
No Desmos needed. We're building an equation, not solving for .
The variable counts small cartons, so more cartons gives the medium count:
- Step 2
Express the large count
Large cartons number times the entire medium count, so multiply by :
The parentheses keep the added inside what gets multiplied.
- Step 3
Write the total equation
The total includes small, medium, and large cartons, so add their counts and set the sum equal to :
- Step 4
Multiply through the parentheses
Distribute the , meaning multiply each part of by :
The comes from .
- Step 5
Combine the counts
Combine like terms, the parts containing , and then combine the two numbers:
Here counts cartons, and counts the additional cartons. So this equation represents the warehouse's total. Choice D.