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A garden-supply company mixes a potting blend from peat, sand, and compost in the ratio 5 : 3 : 2 by weight. To one batch of this blend the company adds 40 kilograms of compost and nothing else, after which compost makes up 1/3 of the batch by weight. What was the weight, in kilograms, of the sand in the batch before the compost was added?
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Correct answer
B
Assign one common unit to the ratio, then set up a single fraction equation that updates both the compost amount and the total.
Write the three parts using a common scale factor k: peat = 5k, sand = 3k, compost = 2k, so the original total is 10k. Adding 40 kilograms of compost changes two things at once: the compost becomes 2k + 40, and the total becomes 10k + 40, since the added weight also joins the batch. The new compost share is 1/3, so:
(2k + 40) / (10k + 40) = 1/3
Cross-multiply: 3(2k + 40) = 10k + 40, which gives 6k + 120 = 10k + 40, so 80 = 4k and k = 20. The sand was 3k = 3(20) = 60 kilograms. Check: the original total is 200 kilograms with 40 kilograms of compost; after adding 40 more kilograms, compost is 80 and the total is 240, and 80/240 = 1/3.
Choice A reports the original compost weight, 2k, instead of the sand weight. Choice C reports the compost weight after the 40 kilograms are added, 2k + 40, instead of the original sand weight. Choice D comes from adding the 40 kilograms only to the compost in the numerator while leaving the total unchanged: solving (2k + 40)/10k = 1/3 gives k = 30, so the sand is read as 3(30) = 90. Choice E reports the peat weight, 5k, instead of the sand weight. Only choice B applies the correct scale factor to the sand after updating both the top and bottom of the fraction.
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