Proportional Reasoning in a Shop Budget
A shop has a monthly consumables budget of $1,200. Last month it spent $450 on abrasives, $300 on fasteners, $210 on lubricants, and $180 on safety supplies, totaling $1,140. This month the shop expects abrasive prices to rise 20%, fastener prices to fall 10%, and lubricant and safety costs to stay flat. The owner also wants to add a $75 monthly calibration service for a torque wrench. She wants to know whether the budget will cover the planned spending and, if not, what single category could be trimmed to stay within budget without cutting safety supplies.
1. Compute the projected total for this month including the calibration service.
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Abrasives: 450 × 1.20 = $540. Fasteners: 300 × 0.90 = $270. Lubricants: $210. Safety: $180. Subtotal = 540 + 270 + 210 + 180 = $1,200. Add calibration $75 → $1,275. The budget is $1,200, so the plan is $75 over.
2. Identify which category can be trimmed and by how much to meet the $1,200 budget without touching safety.
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Safety is protected at $180. The overage is $75. Lubricants at $210 can absorb a $75 cut (to $135) if usage allows, or fasteners can be trimmed from $270 to $195. Abrasives are already up 20% and cutting them risks production. The cleanest answer: reduce lubricants or fasteners by $75, or defer the calibration service. Any single non-safety category can cover the gap if a $75 reduction is realistic.
3. If the owner instead cuts the calibration service and abrasive prices rise only 10%, what is the new total and how much slack remains?
Read the worked answer
Abrasives at 10%: 450 × 1.10 = $495. Fasteners $270, lubricants $210, safety $180. Total = 495 + 270 + 210 + 180 = $1,155. No calibration added. Budget $1,200 − $1,155 = $45 slack remaining.