Question 52·Easy·Linear Inequalities in One or Two Variables
Kamala’s mobile phone plan allows up to gigabytes of data each billing cycle before additional fees apply. Midway through a cycle, she has already used gigabytes. Streaming videos uses about gigabytes per hour.
What is the maximum number of whole hours Kamala can stream videos during the rest of the cycle without incurring additional fees?
For inequality word problems, start by translating words into quantities: find the total allowed amount, subtract what has already been used to get what remains, and then express the new use (here, hours times rate) with an inequality like rate × time ≤ remaining. Solve the inequality for the variable, and if the question asks for whole numbers, choose the largest integer that still satisfies the inequality. Always double-check units (GB vs. hours) and that you’re not forgetting any already-used amount.
Hints
Think about remaining data
You know the total data allowed is GB and she has already used GB. How much data is left for the rest of the cycle?
Write an inequality for hours of streaming
Let be the number of hours she streams. Each hour uses GB. How can you express the condition that her total additional data use, , cannot be more than the data she has left?
Solve and interpret your inequality
After you write the inequality, solve it for . Then think: if must be a whole number, what is the largest whole number that satisfies your inequality?
Desmos Guide
Model the situation with an inequality
In a Desmos expression line, type 0.75h <= 7.5 (or use x instead of h if you prefer). This represents the condition that the streaming data use must not exceed the remaining 7.5 GB.
View the solution range
Look at the number line (if using Desmos scientific calculator) or the shaded region (if using the graphing calculator). Identify the largest whole-number value of the variable that still satisfies the inequality; that value is the maximum number of whole hours she can stream without extra fees.
Alternative check with direct calculation
In another expression line, type (10 - 2.5)/0.75. The output is the maximum number of hours allowed by the data limit; use this value, rounded down if necessary, as the answer.
Step-by-step Explanation
Find how much data she has left
Kamala’s plan allows up to GB, and she has already used GB.
So the remaining data she can use is:
She has GB left for the rest of the cycle.
Relate remaining data to hours of streaming
Streaming videos uses GB per hour.
Let be the number of hours she streams for the rest of the cycle. The data she will use for streaming is GB.
Because she cannot exceed the remaining GB, write the inequality:
Solve the inequality for hours
Solve by dividing both sides by :
This means she can stream up to 10 hours without going over the data limit. Since the question asks for the maximum number of whole hours, the answer is .