A cell phone plan costs 20 dollars each month, plus 5 cents per text message sent, plus 10 cents for each minute used over 30 hours. In January Michelle sent 100 text messages and talked for 30.5 hours. How much did she have to pay?
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Toolkit + CCSS Solution
Understand
Restated: A phone bill has three parts: a flat $20 base, a charge of 5 cents for every text sent, and a charge of 10 cents for every minute of talking beyond 30 hours. Michelle sent 100 texts and talked for 30.5 hours. Find her total bill.
Givens: Base charge: $20 per month; Text charge: 5 cents per text sent; Overage charge: 10 cents per minute used over 30 hours; Michelle sent 100 texts; Michelle talked for 30.5 hours
Unknowns: The total amount Michelle pays for January
Understand
Restated: A phone bill has three parts: a flat $20 base, a charge of 5 cents for every text sent, and a charge of 10 cents for every minute of talking beyond 30 hours. Michelle sent 100 texts and talked for 30.5 hours. Find her total bill.
Givens: Base charge: $20 per month; Text charge: 5 cents per text sent; Overage charge: 10 cents per minute used over 30 hours; Michelle sent 100 texts; Michelle talked for 30.5 hours
Plan
Primary tool: #7 Identify Subproblems
Secondary: #8 Analyze the Units
The bill is a sum of three independent pieces, so I compute each piece by itself and add them. The pieces mix units (cents, dollars, hours, minutes), so I convert carefully as I go to keep everything in dollars.
Execute — Answer: D
#7 Identify Subproblems 4.OA.A.3Step 1
Split the bill into three parts
The total is the base fee plus the texting cost plus the extra-minutes cost.
I will find each part separately and then add them.
💡 Charges start at the cutoff, so subtract the free amount first, then switch to the unit that gets billed.
#8 Analyze the Units 5.NBT.B.7Step 4
Cost of the extra minutes
Each extra minute costs 10 cents, and $10$ cents is $\$0.10$. For 30 minutes, multiply: $30 \times \$0.10 = \$3.00$.
30 \times \$0.10 = \$3.00
💡 Same idea as the texts: rate times amount gives the cost of that piece.
#7 Identify Subproblems 5.NBT.B.7Step 5
Add the three parts
Add the base, the texting cost, and the extra-minutes cost: $\$20 + \$5 + \$3 = \$28$.
Michelle paid $\$28.00$, which is choice (D).
\$20.00 + \$5.00 + \$3.00 = \$28.00
💡 Once every piece is priced in dollars, the total is just their sum.
[1]
#7 4.OA.A.3The total is the base fee plus the texting cost plus the extra-minutes cost. I w
[2]
#8 5.NBT.B.7Each text costs 5 cents, and $5$ cents is $\$0.05$. For 100 texts, multiply: $10
[3]
#8 4.MD.A.1Only time past 30 hours is charged. She talked $30.5$ hours, so the extra is $30
[4]
#8 5.NBT.B.7Each extra minute costs 10 cents, and $10$ cents is $\$0.10$. For 30 minutes, mu
[5]
#7 5.NBT.B.7Add the base, the texting cost, and the extra-minutes cost: $\$20 + \$5 + \$3 =
Review
Reasonableness: The base alone is $20, and two small usage charges of $5 and $3 push the bill up by $8, landing at $28. That is a modest, sensible total for one month, and it matches choice (D). A common slip is charging all 30.5 hours or forgetting to turn 0.5 hour into 30 minutes; guarding against those keeps the extra-minutes cost at exactly $3.
Alternative: Work entirely in cents to avoid decimals: base $= 2000$ cents, texts $= 100 \times 5 = 500$ cents, minutes $= 30 \times 10 = 300$ cents. The sum $2000 + 500 + 300 = 2800$ cents $= \$28.00$, the same answer.
CCSS standards used (min grade 5)
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers (Breaking the bill into a base part, a texting part, and an extra-minutes part, then combining them.)
4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units (Converting the 0.5 hour of overage into 30 minutes so it can be billed per minute.)
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths (Multiplying the cent rates in dollars and adding the three dollar amounts to the total.)
⭐ Price each part of the bill on its own, remember to bill only the time past the cutoff, then add everything up.
⭐ Price each part of the bill on its own, remember to bill only the time past the cutoff, then add everything up.