Examkin

Question

Difficulty: HardSolving Linear Equations

A company offers two monthly data storage plans. Plan A costs 32.00plus32.00 plus 0.08 per gigabyte of data stored. Plan B costs 15.00plus15.00 plus 0.14 per gigabyte for the first 150 gigabytes of data stored, and $0.12 per gigabyte for all data stored beyond the first 150 gigabytes. For how many gigabytes of data stored in a single month would the monthly cost under both plans be exactly the same?

Answer: 350 gigabytes

Answer

The monthly costs under both plans are exactly the same when the data stored is 350 gigabytes.
Equating the two cost functions yields 32+0.08g=15+0.14(150)+0.12(g−150)32 + 0.08g = 15 + 0.14(150) + 0.12(g - 150), which simplifies to 32+0.08g=18+0.12g32 + 0.08g = 18 + 0.12g. Solving for gg gives 0.04g=140.04g = 14, which results in g=350g = 350.

Step-by-Step Solution

1
Determine the cost function for Plan A.
CA(g)=32+0.08gC_A(g) = 32 + 0.08g
Plan A charges a flat fee of 32.00and32.00 and 0.08 per gigabyte.
2
Determine the cost function for Plan B when the usage exceeds 150 gigabytes.
CB(g)=15+0.14(150)+0.12(g−150)=18+0.12gC_B(g) = 15 + 0.14(150) + 0.12(g - 150) = 18 + 0.12g
Plan B charges 15.00flat,15.00 flat, 0.14 per gigabyte for the first 150 gigabytes, and $0.12 per gigabyte for any additional usage.
3
Equate the two cost functions and solve for gg.
32+0.08g=18+0.12g  ⟹  14=0.04g  ⟹  g=35032 + 0.08g = 18 + 0.12g \implies 14 = 0.04g \implies g = 350
To find the usage where both plans cost the same, set their cost functions equal and isolate the variable gg.

Key Concept

Solving linear equations in real-life contexts involving piecewise rates
Rate this question

Topics

Solving Linear Equations

More questions from this topic