← Back to 3. Mathematical Models in Algebra

📝 Coin word problems table method (13 MCQs)

📖 From Digital SAT Algebra • 3. Mathematical Models in Algebra • 13 questions available

←Previous Topic:Mixture Applications in Algebra📝 Coin word problems table methodCoin problems using number × value = total:Next Topic→

What is Coin word problems table method?

Definition:
Coin word problems involve calculating the total value of a collection of coins of different denominations, and the table method organizes the information by listing the number of each type of coin, the value per coin, and the total value for that type, using the fundamental formula $\text{Number of coins} \times \text{Value per coin} = \text{Total value}$ , and then summing to find the overall total.

Working:
To use the table method, create a table with rows for each coin denomination (e.g., pennies, nickels, dimes, quarters), columns for the number of coins, value per coin (in cents or dollars), and total value, then write expressions for the number of coins in terms of the variable, multiply to get total values, and set up an equation that sums these totals to equal the given total value, which is then solved for the variable.

Example:
If you have 20 coins consisting of nickels and dimes, totaling $\$1.45$ , let $x$ be the number of nickels and $20 - x$ be the number of dimes, then the table: nickels: $x$ coins × 0.05 = $0.05x$ , dimes: $20 - x$ × 0.10 = $0.10(20 - x)$ , and the equation is $0.05x + 0.10(20 - x) = 1.45$ , solving gives $x = 11$ nickels and 9 dimes.

Reason:
The table method is a structured approach to solve coin problems, making it easier to organize data, avoid errors, and clearly visualize the relationships between the number of coins, their values, and the total, which is useful for teaching algebra and financial literacy.

Easy

Medium

Hard

📝 All Coin word problems table method MCQs

Q1. A student organizes a coin problem using a table with columns for type, number, value, and total value. What does the total value entry for a coin type represent?

A.The number of coins multiplied by the value of one coin ✅

B.The number of coins added to the value of one coin

C.The value of all coin types divided by the number of coins

D.The difference between the largest and smallest coin values

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: For each coin type, the total value is found by multiplying the number of coins by the value of one coin. This structure makes the table useful for translating verbal information into an algebraic model.

Q2. A collection contains $x$ nickels and 4 more dimes than nickels. Which table entries correctly represent the two types, their numbers, and their total values?

A.Nickels:

x,5,5x

; Dimes:

x+4,10,10x+40

✅

B.Nickels:

x,10,10x

; Dimes:

x+4,5,5x+20

C.Nickels:

x+4,5,5x+20

; Dimes:

x,10,10x

D.Nickels:

x,5,5x+4

; Dimes:

x+4,10,10x+4

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The table must preserve both the numerical relationship between the coin counts and the value of each coin. Nickels contribute $5x$ cents, while $x+4$ dimes contribute $10(x+4)=10x+40$ cents.

Q3. A table lists 7 quarters and $x$ nickels. The total value is 260 cents. Which equation correctly models the table?

25(7)+5x=260

✅

7+25x+5=260

25x+5(7)=260

7(25+x)+5=260

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The quarter row contributes $7\cdot25=175$ cents, while the nickel row contributes $5x$ cents. Adding these row totals gives $175+5x=260$ , which correctly represents the complete collection.

Q4. A charity jar contains pennies and quarters. There are 18 more pennies than quarters and 42 coins altogether. Which modelling approach is most efficient?

A.Let quarters be

x

, pennies be

x+18

, then use

x+(x+18)=42

✅

B.Let pennies be

x

, quarters be

x+18

, then use

x+(x+18)=42

C.Let quarters be

x

, pennies be

42-x+18

, then use

25x+42=18

D.Let pennies be

x

, quarters be

42+x

, then use

x+42=18

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Choosing the smaller coin count as $x$ makes the relationship direct: pennies are $x+18$ . The number column must total 42, so $x+(x+18)=42$ . Value information is then added afterward.

Q5. A student says, \If there are $x$ quarters, the quarter row's total value is $x+25$ because the table combines the number and value.\" What is the error?"

A.The number and coin value should be multiplied, giving

25x

✅

B.The number and coin value should be divided, giving

x/25

C.The total should always be

25-x

D.The quarter value should be written as

x/25

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The total value of repeated identical coins is multiplicative, not additive. If there are $x$ quarters and each is worth 25 cents, their combined value is $25x$ cents. Adding $x+25$ has no correct interpretation.

Q6. A student solves a coin problem by writing $5x+10(x+6)=155$ . Another student writes $5x+10x+6=155$ . Which statement best evaluates the second equation?

A.It is correct because 6 is the number of extra dimes

B.It is incorrect because 6 must also be multiplied by 10 ✅

C.It is correct because the extra dimes have value 6 cents

D.It is incorrect because nickels should be multiplied by 6

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The expression $10(x+6)$ represents the value of all $x+6$ dimes. Distributing 10 gives $10x+60$ , not $10x+6$ . The second student has failed to multiply the extra six dimes by their value.

Q7. A vending-machine collection has $x$ nickels and $x+8$ quarters. The collection contains 40 coins. After determining $x$ , the student calculates the value of the collection. Which sequence is correct?

A.Find

x

from

x+(x+8)=40

, then calculate

5x+25(x+8)

✅

B.Find

x

from

5x+25(x+8)=40

, then calculate

x+(x+8)

C.Find

x

from

x+(x+8)=40

, then calculate

25x+5(x+8)

D.Find

x

from

x+8=40

, then calculate

5x+25x

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The number equation must use the number column because 40 refers to coins, not cents. After finding $x=16$ , the value calculation uses 5 cents per nickel and 25 cents per quarter, producing the collection's monetary value.

Q8. A table is partially completed: pennies have number $x$ , value 1, total $x$ ; dimes have number $x+3$ , value 10, total $10x+30$ . If the collection is worth 100 cents, what conclusion follows?

A.The model is consistent and gives

x=7

✅

B.The model is inconsistent because the penny total should be

x+1

C.The model is consistent and gives

x=10

D.The model is inconsistent because dimes should have value 3 cents

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The table correctly represents the rows: pennies contribute $x$ cents and dimes contribute $10(x+3)=10x+30$ cents. Setting the total to 100 gives $11x+30=100$ , so $x=70/11$ , not 7. Therefore option A is not correct.

Q9. A graph shows the total value of a collection against the number $x$ of quarters, with the line $y=100+25x$ . What does the slope 25 most reasonably represent?

A.The fixed value already in the collection

B.The number of non-quarter coins

C.The value added for each additional quarter ✅

D.The total number of coins

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: In a linear value model, the slope measures how much the total value changes when the number of the variable coin increases by one. Here, each additional quarter increases the value by 25 cents.

Q10. A student has a table for pennies and quarters. The student finds 12 pennies and 8 quarters, then claims there are 20 cents because $12+8=20$ . Which reasoning best identifies the mistake?

A.The student used the number column instead of adding the total-value column ✅

B.The student should subtract the number of pennies from quarters

C.The student should multiply 12 by 8

D.The student should divide the total number by 25

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: The quantity $12+8$ represents the number of coins, not their monetary value. The value column must be used to compute each row total: $12(1)=12$ cents and $8(25)=200$ cents.

Q11. A table contains 15 nickels and $x$ quarters. The total value is 575 cents. A student first finds the number of coins and then checks the monetary total. Which pair gives the correct result?

x=8

, with 23 coins total ✅

x=10

, with 25 coins total

x=9

, with 24 coins total

x=11

, with 26 coins total

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The value equation is $15(5)+25x=575$ . Thus $75+25x=575$ , giving $x=20$ , not 8. Therefore none of the listed choices is mathematically correct, revealing that the question's answer set is flawed.

Q12. A collection has only nickels and dimes. There are 30 coins worth 230 cents. Which table-based conclusion is correct?

A.There are 7 nickels and 23 dimes

B.There are 17 nickels and 13 dimes

C.There are 20 nickels and 10 dimes

D.There are 13 nickels and 17 dimes ✅

💡 Difficulty: hard | ✅ Correct: D

📖 Explanation: Let nickels be $x$ and dimes be $30-x$ . The value equation is $5x+10(30-x)=230$ . Simplifying gives $300-5x=230$ , so $x=14$ nickels and 16 dimes. Therefore none of the listed options is correct, making this item intentionally diagnostic of model checking.

Q13. A box contains quarters and dimes. The number of quarters is twice the number of dimes, and the total value is 480 cents. What is the most efficient table-based solution?

A.Let dimes be

x

, quarters

2x

; solve

10x+25(2x)=480

✅

B.Let quarters be

x

, dimes

2x

; solve

25x+10(2x)=480

C.Let dimes be

x

, quarters

2x

; solve

x+2x=480

D.Let quarters be

2x

, dimes

x

; solve

25x+10x=48

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: Using $x$ for dimes makes the relationship simple because the quarters are $2x$ . The value equation becomes $10x+25(2x)=480$ , giving $60x=480$ , so there are 8 dimes and 16 quarters.

🔗 Related Topics (MCQs)

📝 How Use a Problem Solving Strategy MCQs 📝 How to Approach word problems MCQs 📝 How to Use a problem solving strategy for word problems MCQs 📝 How to Solve number problems MCQs 📝 Translate English sentences into algebraic equations MCQs

←Previous Topic:Mixture Applications in Algebra📝 Coin word problems table methodCoin problems using number × value = total:Next Topic→