SME
Grade 9 Math · Problem type
Whole-number answers
Use this for “$12 to join plus $4 a visit, and at most $50. How many visits?”
Diagram
v <
v ≤
v >
v ≥
v ≤ 9.5: every number less than or equal to 9.5.
The closed circle takes in 9.5.
Fixed cost: $12
Cost per visit: $4
Budget: $50
This is an example. Type your own values to start a new problem.
$
F
+
$
p
v
$
B
n
Bound on the visits
worked out (not typed)
N
Most or fewest whole visits
worked out (not typed)
Formulas
n
=
B
−
F
p
9.5
=
50 − 12
4
N
=
n
rounded
to
a
whole
number,
down
or
up
as
s
says
9 = 9.5 rounded to a whole number, down or up as ≤ says
Assumptions
•
Write the story as an inequality: fixed cost + cost per visit × visits ≤ budget.
•
Solve it as an equation, then keep the sign.
•
Visits come in whole numbers: round down for at most, up for at least.
Step-by-step
WE KNOW
F = $12, p = $4, s: ≤, B = $50
FIND
bound on the visits (n), most or fewest whole visits (N)
Step 1 · Find bound on the visits (n)
Use n = (B − F) ÷ p
Take the fixed cost from both sides, then divide by the cost per visit: the sign stays.
n
=
50 − 12
4
n
=
38
4
n
=
9.5
Step 2 · Find most or fewest whole visits (N)
Use N = n rounded to a whole number, down or up as s says
At most: the most whole visits at or below the bound.
N
=
n
rounded
down
to
a
whole
number
N
=
9.5
rounded
down
to
a
whole
number
12 + 4 × 9 = 48, at most 50
12 + 4 × 10 = 52, more than 50
N
=
9
Check
Put the numbers back in. Both sides should match.
9.5
=
50 − 12
4
✓
12 + 4 × 9 ≤ 50 ✓
Topic check
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