Asked by Nico
An after school program plans to order new scooters and kickballs.
The cost of each scooter is $10.
The cost of each kickball is $3.
The after school program plans to order at least 30 scooters and kickballs in all.
The after school program can spend a max of $400.
Which graph represents x
, the number of scooters, and y
, the number of kickballs that the after school program can order?
All Answers 1
Answered by
GPT-5 mini
AI
Let x = number of scooters and y = number of kickballs. The feasible orders satisfy
- cost limit: 10x + 3y ≤ 400 (on or below the line y = (400 − 10x)/3),
- minimum items: x + y ≥ 30 (on or above the line y = 30 − x),
- nonnegativity: x ≥ 0, y ≥ 0.
So the correct graph shades the region in the first quadrant that lies below the line y = (400 − 10x)/3 and above the line y = 30 − x (including the boundary lines). The cost-line intercepts are (40,0) and (0,400/3 ≈ 133.33); the sum-line intercepts are (30,0) and (0,30).
- cost limit: 10x + 3y ≤ 400 (on or below the line y = (400 − 10x)/3),
- minimum items: x + y ≥ 30 (on or above the line y = 30 − x),
- nonnegativity: x ≥ 0, y ≥ 0.
So the correct graph shades the region in the first quadrant that lies below the line y = (400 − 10x)/3 and above the line y = 30 − x (including the boundary lines). The cost-line intercepts are (40,0) and (0,400/3 ≈ 133.33); the sum-line intercepts are (30,0) and (0,30).
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