Also in 2026 Practice Test B Math, question 38; 2025 Practice Test B Math, question 45.
Question
Phan chose an Internet service that charges $18.00 per month plus $0.024 per minute. Deion chose an Internet service that charges $30.00 per month for unlimited usage. At the end of the month, Phan’s and Deion’s charges were identical. For how many minutes did Phan use the Internet service that month?
- A50
- B60
- C100
- D500
Show the answer
Correct answer: D
Let x be the number of minutes Phan used his internet service in the month. Phan’s monthly charges were
18 + 0.024x
Since Deion’s charges were the same as Phan’s, set the expression equal to 30 and solve for x:
18 + 0.024x = 30
0.024x = 12
x = 500
Phan used his service for 500 minutes.
Question analysis
Phan pays $18 a month plus 2.4 cents per minute for Internet service, Deion pays a flat $30, and their bills come out the same. Students find how many minutes Phan used. It tests writing and solving a two-step linear equation, and the small decimal rate makes the division error-prone.
- NYS standards
- 7.EE.4a two-step equations
- Grade level
- Grade 7 content, by NYS standard
- Compared with grade 7
- At grade 7 Solving equations of the form px + q = r from a word problem is central grade 7 work. This is a typical example; only the three-decimal-place rate adds some care to the division.
- Estimated difficulty
- Straightforward: two steps or one careful reading.
- Thinking it demands
- Depth of knowledge 2, skills and concepts · mainly apply
- What makes it hard
- Error-prone arithmetic moderate
- Turning words into math minor
- Solution
- 3 steps
- Reading level
- Question and choices: about grade 5, 48 words.
- Students, last 30 days
- Not enough answers yet to show (it takes 10).
Why it is hard, traps and wrong answers (shows the answer)
Why it is hard
Setting up the equation is routine, so the question is mostly a test of decimal division. Dividing 12 by 0.024 invites a misplaced decimal point, and one such slip gives a choice exactly ten times too small. A quick check, 500 × 0.024 = 12, confirms the answer in seconds.
Error-prone arithmetic moderate Working it out
The last step divides 12 by 0.024, a three-place decimal, and moving the decimal point one place too few gives 50 instead of 500. (Brown & Burton, 1978; Junker & Sijtsma, 2001)
Turning words into math minor Understanding the question
"Phan's and Deion's charges were identical" has to become 18 + 0.024m = 30, with the flat $30 on one side and Phan's fee plus per-minute cost on the other. (Hegarty, Mayer & Monk, 1995; Koedinger & Nathan, 2004)
Strategy: Set Phan's cost, the monthly fee plus the per-minute charge times the minutes, equal to Deion's flat fee, then subtract and divide, checking the decimal places.
Traps
- An arithmetic slip: The right method with a plausible arithmetic error: a digit, a place value or a times-table fact.
The wrong answers, classified
A An arithmetic slip (Junker & Sijtsma, 2001)
Divides 12 by 0.024 but shifts the decimal point one place too few, as if the rate were 24 cents a minute: 12 ÷ 0.24 = 50.
B Little reason to choose it (Haladyna & Downing, 1993; Rodriguez, 2005)
No step with the $12 gap and the $0.024 rate gives 60; it most likely attracts students thinking of the 60 minutes in an hour.
C Little reason to choose it (Haladyna & Downing, 1993; Rodriguez, 2005)
No computation from the given numbers yields 100, and 100 minutes would add only $2.40 to Phan's $18 fee.
Worked solution, step by step
Formulas used
- Cost with a monthly fee
- C is the total cost for the month. f is the fixed fee you pay no matter what. r is the price for each minute, and m is the number of minutes. Use it when a bill has a set fee plus a charge for each unit.
Sort out what you know
Phan pays $18.00 a month plus $0.024 for each minute. Deion pays $30.00 a month, however much he uses. Their bills were the same. You need the number of minutes Phan used. Call it .
Write an equation
Use the cost formula for Phan. His bill equals Deion’s $30.
An equation says two amounts are equal. Here it says the two bills are equal.
Take away the monthly fee
Subtract 18 from both sides. That leaves the minutes part alone.
So Phan paid $12 for his minutes.
Divide to find the minutes
Divide 12 by 0.024. To get rid of the decimal, move the point 3 places right in both numbers.
Phan used 500 minutes.
Watch out: 0.024 is not 0.24. Using 0.24 gives , choice A. Move the point the same number of places in both numbers.
Give the answer
Phan used 500 minutes that month. That is the only choice that makes the two bills equal. So the answer is D, 500.
Check your answer
Put 500 back in. The minutes cost dollars. Add the fee: dollars. That is Deion’s bill, so the bills match.
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