Two part-to-part ratios describe different groups: fragile versus nonfragile boxes across both trucks, then fragile boxes on A versus B. First find the total number of fragile boxes. Use the second ratio to find B’s lead in fragile boxes, then subtract the fragile lead from the total-box lead. Don’t assume each truck has the same fragile fraction as the combined shipment.
Hints
- Hint 1
A part-to-part ratio compares two separate groups. The fragile and nonfragile boxes together make up all the boxes, so add the ratio parts before finding the fraction that is fragile.
- Hint 2
The ratio splits only the fragile boxes between the trucks. It gives A equal parts and B equal parts. How many of those parts is B ahead?
- Hint 3
Each truck’s total includes fragile and nonfragile boxes. To find B’s nonfragile lead, start with its lead in all boxes and remove its lead in fragile boxes.
Step-by-step
Subtract the fragile difference
Step 1Find the fragile share of all boxes
The part-to-part ratio compares fragile with nonfragile boxes across both trucks combined. Those groups make parts altogether, so the fragile share of all boxes is . Using would compare fragile boxes with nonfragile boxes, not with the whole shipment.
- Step 2
Count the fragile boxes
Type , where is the fragile-box count across both trucks. Desmos shows .
- Step 3
Find B’s lead in all boxes
Type , where is B’s total-box lead over A. Desmos shows . This counts fragile and nonfragile boxes together.
- Step 4
Find B’s lead in fragile boxes
The ratio splits the fragile boxes into equal parts. B has more of those parts than A. Type . Desmos shows , B’s lead in fragile boxes.
- Step 5
Find B’s lead in nonfragile boxes
B’s extra boxes are either fragile or nonfragile, so remove its fragile lead from its total lead. Type ; Desmos shows . Truck B has 140 more nonfragile boxes than Truck A. Choice B.