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15 multiple-choice questions and 18 flashcards on Multi-Step Real-World Problems, about 10% of the 7th Math: Expressions & Equations bank. Every one carries a written rationale.
Multi-Step Real-World Problems is one of 5 chapters in CoStudy's 7th Math: Expressions & Equations bank, and it holds 15 of the bank's 150 multiple-choice questions — roughly 10% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
A book is $15. With 6% sales tax, total?
Answer: C — $15.90
C) 15 × 1.06 = $15.90. B) Added 6 directly. D) Used 4% by mistake. A) Used 10%.
3 less than 4 times a number is 21. Find the number.
Answer: D — 6
D) 4n − 3 = 21 → 4n = 24 → n = 6. A) Solved 4n = 20. C) Divided 18 by 4. B) Set n = 21 − 3.
A car rental is $25/day plus $0.20/mile. Cost for 3 days, 100 miles?
Answer: D — $95
D) 25·3 + 0.20·100 = 75 + 20 = $95. B) Forgot the mile charge. C) Used only mile rate. A) Used 0.50/mile by mistake.
A meal costs $24 and you tip 15%. Total?
Answer: A — $27.60
A) Tip = 24 × 0.15 = $3.60; total = $27.60. B) Used 50%. C) Used 6.25%. D) Added 15 cents.
A car travels at 60 mph for t hours. The distance d is:
Answer: C — d = 60t
C) Distance = rate × time. A/B) Added/subtracted units. D) Inverted the relationship.
You start with $20 and spend $3 per day. Days until $5 left?
Answer: D — 5
D) 20 − 3d = 5 → 3d = 15 → d = 5. A) Off by one (4 days leaves $8). C) 6 days leaves $2. B) Solved differently.
Sam's age plus twice his sister's age = 27. Sister is 9. How old is Sam?
Answer: B — 9
B) Sam + 2(9) = 27 → Sam + 18 = 27 → Sam = 9. A) Computed 2 × 9 only. C) Multiplied 27 + 9. D) Divided 27 by 2.
Solve: 2x + 5 = 17
Answer: D — x = 6
D) Subtract 5: 2x = 12; divide by 2: x = 6. A) Subtracted only. B) Forgot to divide. C) Used wrong divisor.
You have $50. Each ticket costs $7. What is the max number you can buy?
Answer: B — 7
B) 7x ≤ 50 → x ≤ 7.14, so max integer 7. A) Was off by one (rounded down to 6). C) Rounded up incorrectly. D) Subtracted 7 from 50 then divided.
A coat is $80 with 25% off. Sale price?
Answer: D — $60
D) Discount = 80 × 0.25 = $20; sale = 80 − 20 = $60. A) Used 30% off. C) Gave the discount, not the sale price. B) Added the discount.
4 cards from the 18 in this chapter.
Worked Example: Sam's age plus twice his sister's age equals 27. Sister is 9. How old is Sam?
Step 1: Define the variable — let S = Sam's age. Step 2: Translate into an equation. "Sam's age plus twice his sister's age = 27" with sister's age = 9: S + 2(9) = 27. Step 3: Compute 2(9) = 18, so S + 18 = 27. Step 4: Subtract 18: S = 27 − 18 = 9. Step 5: Check: 9 + 2(9) = 9 + 18 = 27 ✓. Answer: Sam is 9 years old.
Word: 5 less than twice a number is 13. Find the number.
9. (2x − 5 = 13; 2x = 18; x = 9.)
Word: A movie ticket is $10 + $3 per snack. With $25, how many snacks?
At most 5. (10 + 3x ≤ 25; x ≤ 5.)
Word: 3 friends share equally a $42 bill plus a $6 tip. Each pays?
$16. ((42 + 6)/3 = 48/3 = 16.)
These are a sample. The full Multi-Step Real-World Problems chapter runs 33 items with per-chapter progress tracking, on the web and in the iOS app.
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