Dosing a Cleaning Solution from a Concentrate
A custodian must mix a disinfectant from concentrate. The label says the working solution must be 1 part concentrate to 63 parts water (a 1:64 dilution). The sprayer tank holds 1.5 gallons. A 32-fluid-ounce bottle of concentrate costs $11.40 and the custodian mixes a fresh tank whenever the previous one is empty. The custodian works 5 days a week and uses exactly 2 tanks per day. One fluid ounce = 1/128 gallon. A bulk 1-gallon jug of concentrate costs $38.00. Management wants the lowest annual cost assuming 50 working weeks per year.
1. How many fluid ounces of concentrate go into one 1.5-gallon tank, and how many tanks can one 32-oz bottle make?
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Tank = 1.5 gal × 128 = 192 fl oz. Concentrate fraction = 1/64. Concentrate per tank = 192 ÷ 64 = 3 fl oz. Bottle of 32 oz makes 32 ÷ 3 = 10.67 → 10 full tanks (with 2 oz left over).
2. Compute annual concentrate cost using the 32-oz bottles versus the 1-gallon bulk jug, and recommend the cheaper option.
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Tanks per year = 2/day × 5 days × 50 weeks = 500 tanks. Concentrate needed = 500 × 3 = 1500 fl oz. Bottles: 1500 ÷ 32 = 46.9 → 47 bottles × $11.40 = $535.80. Bulk: 1 gal = 128 oz; 1500 ÷ 128 = 11.7 → 12 jugs × $38.00 = $456.00. Bulk is cheaper by $79.80/year. Recommend the 1-gallon jugs.
3. The custodian accidentally mixes 1:32 instead of 1:64. How much concentrate is wasted per tank and what is the annual cost impact at bulk pricing?
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At 1:32, concentrate per tank = 192 ÷ 32 = 6 fl oz, double the correct 3 oz. Waste = 3 fl oz per tank. Over 500 tanks, extra concentrate = 1500 fl oz. At bulk price, cost per oz = $38.00 ÷ 128 = $0.2969. Extra cost = 1500 × 0.2969 = $445.31 extra per year, roughly doubling concentrate spend. This also risks surface damage from over-strength solution, so the mixing ratio should be enforced.