If 30 boxes were stacked beside each other in a row, the length of the row would be approximately five and seven-ninths inches. At this rate, which of the following is closest to the number of boxes it would take to make a nine-inch-long row? A) 45, B) 175, C) 16, or D) 20.
In five and seven-ninths inches, there were 30 boxes. Approximately, how many boxes would it take to make a nine-inch row? Well, it certainly couldn’t take less than the boxes that it took to make a 30-inch row. We know that it wouldn’t be 16 or 20. Also imagine if we double the number of boxes. If we added 30 more boxes and we said that five and seven-ninths inches is about six inches, then we could say that 60 boxes take up about 12 inches. And if 60 boxes take up about 12 inches, there’s no way that 175 boxes would make nine inches. And so we’ve narrowed it down to option A, 45 boxes.
To check this, we could set up a ratio. 30 boxes, and we’ll round five and seven-ninths inches to six inches, is equal to 𝑥 boxes in nine inches. To solve this one, we cross multiply 30 by nine and six times 𝑥. 30 times nine equals 270. And if we then divided both sides by six, 270 divided by six equals 45. It would take about 45 boxes to make a nine-inch-long row.