SME
Grade 9 Math · Problem type
Square units and a cost
Use this for “Carpet costs $30 a square yard. What does it cost for a 12 ft by 15 ft room?”
Diagram
Struck through: ft², each on a top and a bottom, so they cancel.
The unit left is yd².
Each factor is 1 (its top and bottom are the same amount), so the amount does not change.
This is an example. Type your own values to start a new problem.
l (ft)
×
w (ft)
=
Aft (ft²)
=
Ayd (yd²)
Ayd (yd²)
×
$
p
=
$
C
Formulas
Aft
=
l
×
w
180 = 15 × 12
Ayd
=
Aft
×
1
9
20
=
180
×
1
9
C
=
p
×
Ayd
600 = 30 × 20
Assumptions
•
1 yd = 3 ft, so 1 yd² = 3 ft × 3 ft = 9 ft²: square the length factor.
•
The price is per square yard, so change the area to square yards before multiplying.
Step-by-step
WE KNOW
l = 15 ft, w = 12 ft, p = $30
FIND
area in square feet (Aft), area in square yards (Ayd), cost (C)
Step 1 · Find area in square feet (Aft)
Use Aft = l × w
The floor’s area is its length times its width.
Aft = 15 × 12
Aft = 180 ft²
Step 2 · Find area in square yards (Ayd)
Use Ayd = Aft × 1/9
Multiply by 1 yd² per 9 ft²: the ft² cancel, leaving square yards.
Ayd
=
Aft
9
Ayd
=
180
9
Ayd = 20 yd²
Step 3 · Find cost (C)
Use C = p × Ayd
Dollars per square yard times square yards: the yd² cancel, leaving dollars.
C
=
30
×
20
C
=
$600
Check
Put the numbers back in. Both sides should match.
180 = 15 × 12 ✓
20
=
180
×
1
9
✓
600 = 30 × 20 ✓
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