SME
Grade 9 Math · Problem type
A phone plan with extra data
Use this for “$30 a month covers 5 GB; each GB past that costs $8. What does 8 GB cost?”
Chart
C(8) = 54
This is an example. Type your own values to start a new problem.
F
Plan fee
example · $
L
Included data
example · GB
r
Extra rate per GB
example · $
u
Data used
example · GB
C
Cost
calculated · $
Formulas
C
=
F
if
u
≤
L
,
F
+
r
×
(
u
−
L
)
if
u
>
L
54 = 30 if 8 ≤ 5, 30 + 8 × (8 − 5) if 8 > 5
Assumptions
•
Up to the included amount the cost is the plan fee: a flat piece.
•
Past it, each unit more adds the extra rate: C = F + r(u − L).
•
To find the use from a cost above the fee, undo the second piece.
Step-by-step
WE KNOW
u = 8 GB, F = $30, L = 5 GB, r = $8
FIND
cost (C)
Step 1 · Find cost (C)
Use C = F if u ≤ L, F + r × (u − L) if u > L
Past the included data: the fee plus the rate for each GB over.
C
=
F
+
r
×
(
u
−
L
)
C
=
30
+
8
×
(8
−
5)
C
=
30
+
8
×
3
C
=
30
+
24
C
=
$54
Check
Put the numbers back in. Both sides should match.
54 = 30 + 8 × (8 − 5) ✓
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