Card 1 of 20
EasyStudy card 1
Prompt
What relationship gives total value?
Check the units.
Answer
Number of items multiplied by value per item.
Example
\(8\) items at \(\$6\) each have total value \(8(6)=48\) dollars.
MathChapter 5: Word Problems in Real-Life Situations
Flashcards
Solving Word Problems with Equations Flashcards
Twenty focused cards on total value, profit, distance-rate-time, equal-distance trips, capacities, units, and contextual checks.
Current card1 / 20
Session progress0 of 20 studied
Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is the profit formula?
Include fixed and variable costs.
Answer
\(\text{profit}=\text{revenue}-\text{total cost}\).
Example
Revenue \(500\) minus cost \(320\) gives profit \(180\).
Card 3 of 20
EasyStudy card 3
Prompt
How is revenue calculated for identical items?
Use sold quantity, not always purchased quantity.
Answer
Quantity sold multiplied by selling price per item.
Example
If \(x-4\) items sell for \(9\) dollars, revenue is \(9(x-4)\).
Card 4 of 20
EasyStudy card 4
Prompt
What formula relates distance, rate, and time?
Distance is rate times time.
Answer
\(d=rt\).
Example
At \(50\) mph for \(3\) hours, distance is \(150\) miles.
Card 5 of 20
EasyStudy card 5
Prompt
How do you solve \(d=rt\) for time?
Divide distance by rate.
Answer
\(t=d/r\).
Example
Traveling \(120\) miles at \(40\) mph takes \(3\) hours.
Card 6 of 20
MediumStudy card 6
Prompt
How do you solve \(d=rt\) for rate?
Divide distance by time.
Answer
\(r=d/t\).
Example
\(84\) kilometers in \(2\) hours is \(42\) km/h.
Card 7 of 20
MediumStudy card 7
Prompt
What must be true for an out-and-back trip along the same route?
Speeds and times may differ.
Answer
The outbound and return distances are equal.
Example
Write \(r_1t_1=r_2t_2\).
Card 8 of 20
MediumStudy card 8
Prompt
Are outbound and return travel times automatically equal?
Use \(t=d/r\).
Answer
No. Equal distances at different rates require different times.
Example
The slower return segment takes longer.
Card 9 of 20
MediumStudy card 9
Prompt
Why is \((r_1+r_2)/2\) usually wrong for equal-distance average speed?
Average speed is total distance divided by total time.
Answer
The vehicle spends different amounts of time at the two rates.
Example
Equal distances weight the slower rate for more time.
Card 10 of 20
MediumStudy card 10
Prompt
How do you handle a per-hour rate with time in minutes?
Divide minutes by \(60\).
Answer
Convert minutes to hours before using \(d=rt\).
Example
\(45\) minutes is \(0.75\) hour.
Card 11 of 20
MediumStudy card 11
Prompt
What is a useful variable choice for a total-count problem?
One variable must control all unknown expressions.
Answer
Choose one unknown count and express every related count in terms of it.
Example
If the larger count is \(12\) more, use \(x+12\).
Card 12 of 20
MediumStudy card 12
Prompt
What equation structure models a remaining quantity?
Keep all terms in the same unit.
Answer
Starting quantity minus amounts used or removed equals the remainder.
Example
\(500-25d=175\).
Card 13 of 20
MediumStudy card 13
Prompt
How should sequential percentage changes be applied?
Do not reuse the original amount unless stated.
Answer
Apply each change to the current amount in the stated order.
Example
After a \(20\%\) reduction, the current amount is \(0.8\) times the original.
Card 14 of 20
MediumStudy card 14
Prompt
What is a common profit-equation trap?
Build complete revenue and cost expressions.
Answer
Subtracting unit prices while ignoring quantities, unsold items, or fixed costs.
Example
Use \(12(x-5)-7x\), not simply \(12-7\).
Card 15 of 20
MediumStudy card 15
Prompt
What does a fraction such as three fifths full describe?
Multiply the total by the fraction.
Answer
Three fifths of the unknown total capacity.
Example
If \(48\) liters is three fifths full, \(3c/5=48\).
Card 16 of 20
MediumStudy card 16
Prompt
How do you model a head-start catch-up problem?
One traveler has extra time or distance.
Answer
Set the two traveled distances equal at the catch-up time, including the head start.
Example
\(60t=48(t+0.5)\).
Card 17 of 20
MediumStudy card 17
Prompt
What check follows a whole-item equation?
Do not silently round an incompatible result.
Answer
Verify the solution is a nonnegative whole number and satisfies the original totals.
Example
A solution of \(14.5\) tickets signals inconsistent data.
Card 18 of 20
MediumStudy card 18
Prompt
Why can the solved variable be only an intermediate answer?
Re-read the final sentence.
Answer
The question may ask for a related distance, cost, count, or remainder.
Example
After finding time, multiply by rate if distance is requested.
Card 19 of 20
MediumStudy card 19
Prompt
What verifies a one-variable word-problem solution?
Check the story, not only the simplified equation.
Answer
Substitute it into every original relationship and confirm units and totals.
Example
Purchased count, sold count, revenue, cost, and profit should all agree.
Card 20 of 20
HardStudy card 20
Prompt
What should be organized separately in a multi-stage travel problem?
A table prevents mixing stages.
Answer
Each segment's rate, time, and distance, plus any rest time.
Example
Total elapsed time includes travel times and stated stops.
Deck complete
You rated every card. Revisit difficult cards or shuffle for another pass.
Keyboard: Space reveals, left/right arrows navigate, 1–4 rate, and S shuffles.